Daily Papers

In this paper, we present a diffusion model-based framework for animating people from a single image for a given target 3D motion sequence. Our approach has two core components: a) learning priors about invisible parts of the human body and clothing, and b) rendering novel body poses with proper clothing and texture. For the first part, we learn an in-filling diffusion model to hallucinate unseen parts of a person given a single image. We train this model on texture map space, which makes it more sample-efficient since it is invariant to pose and viewpoint. Second, we develop a diffusion-based rendering pipeline, which is controlled by 3D human poses. This produces realistic renderings of novel poses of the person, including clothing, hair, and plausible in-filling of unseen regions. This disentangled approach allows our method to generate a sequence of images that are faithful to the target motion in the 3D pose and, to the input image in terms of visual similarity. In addition to that, the 3D control allows various synthetic camera trajectories to render a person. Our experiments show that our method is resilient in generating prolonged motions and varied challenging and complex poses compared to prior methods. Please check our website for more details: https://boyiliee.github.io/3DHM.github.io/.

Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive generative capabilities that have been used to correct corruptions in images, and the similarities between "in-painting" and filling in missing nodes and edges conditioned on the observed graph, we propose a novel graph generative framework, SGDM, which is based on subgraph diffusion. Our framework not only improves the scalability and fidelity of graph diffusion models, but also leverages the reverse process to perform novel, conditional generation tasks. In particular, through extensive empirical analysis and a set of novel metrics, we demonstrate that our proposed model effectively supports the following refinement tasks for partially observable networks: T1: denoising extraneous subgraphs, T2: expanding existing subgraphs and T3: performing "style" transfer by regenerating a particular subgraph to match the characteristics of a different node or subgraph.

Diffusion Language Models (DLMs) have emerged as a promising new paradigm for text generative modeling, potentially addressing limitations of autoregressive (AR) models. However, current DLMs have been studied at a smaller scale compared to their AR counterparts and lack fair comparison on language modeling benchmarks. Additionally, training diffusion models from scratch at scale remains challenging. Given the prevalence of open-source AR language models, we propose adapting these models to build text diffusion models. We demonstrate connections between AR and diffusion modeling objectives and introduce a simple continual pre-training approach for training diffusion models. Through systematic evaluation on language modeling, reasoning, and commonsense benchmarks, we show that we can convert AR models ranging from 127M to 7B parameters (GPT2 and LLaMA) into diffusion models DiffuGPT and DiffuLLaMA, using less than 200B tokens for training. Our experimental results reveal that these models outperform earlier DLMs and are competitive with their AR counterparts. We release a suite of DLMs (with 127M, 355M, and 7B parameters) capable of generating fluent text, performing in-context learning, filling in the middle without prompt re-ordering, and following instructions https://github.com/HKUNLP/DiffuLLaMA.

Image inpainting task refers to erasing unwanted pixels from images and filling them in a semantically consistent and realistic way. Traditionally, the pixels that are wished to be erased are defined with binary masks. From the application point of view, a user needs to generate the masks for the objects they would like to remove which can be time-consuming and prone to errors. In this work, we are interested in an image inpainting algorithm that estimates which object to be removed based on natural language input and removes it, simultaneously. For this purpose, first, we construct a dataset named GQA-Inpaint for this task. Second, we present a novel inpainting framework, Inst-Inpaint, that can remove objects from images based on the instructions given as text prompts. We set various GAN and diffusion-based baselines and run experiments on synthetic and real image datasets. We compare methods with different evaluation metrics that measure the quality and accuracy of the models and show significant quantitative and qualitative improvements.

With the advancements in denoising diffusion probabilistic models (DDPMs), image inpainting has significantly evolved from merely filling information based on nearby regions to generating content conditioned on various prompts such as text, exemplar images, and sketches. However, existing methods, such as model fine-tuning and simple concatenation of latent vectors, often result in generation failures due to overfitting and inconsistency between the inpainted region and the background. In this paper, we argue that the current large diffusion models are sufficiently powerful to generate realistic images without further tuning. Hence, we introduce PILOT (inPainting vIa Latent OpTimization), an optimization approach grounded on a novel semantic centralization and background preservation loss. Our method searches latent spaces capable of generating inpainted regions that exhibit high fidelity to user-provided prompts while maintaining coherence with the background. Furthermore, we propose a strategy to balance optimization expense and image quality, significantly enhancing generation efficiency. Our method seamlessly integrates with any pre-trained model, including ControlNet and DreamBooth, making it suitable for deployment in multi-modal editing tools. Our qualitative and quantitative evaluations demonstrate that PILOT outperforms existing approaches by generating more coherent, diverse, and faithful inpainted regions in response to provided prompts.

Predicting and anticipating future outcomes or reasoning about missing information in a sequence are critical skills for agents to be able to make intelligent decisions. This requires strong, temporally coherent generative capabilities. Diffusion models have shown remarkable success in several generative tasks, but have not been extensively explored in the video domain. We present Random-Mask Video Diffusion (RaMViD), which extends image diffusion models to videos using 3D convolutions, and introduces a new conditioning technique during training. By varying the mask we condition on, the model is able to perform video prediction, infilling, and upsampling. Due to our simple conditioning scheme, we can utilize the same architecture as used for unconditional training, which allows us to train the model in a conditional and unconditional fashion at the same time. We evaluate RaMViD on two benchmark datasets for video prediction, on which we achieve state-of-the-art results, and one for video generation. High-resolution videos are provided at https://sites.google.com/view/video-diffusion-prediction.

Video outpainting aims to adequately complete missing areas at the edges of video frames. Compared to image outpainting, it presents an additional challenge as the model should maintain the temporal consistency of the filled area. In this paper, we introduce a masked 3D diffusion model for video outpainting. We use the technique of mask modeling to train the 3D diffusion model. This allows us to use multiple guide frames to connect the results of multiple video clip inferences, thus ensuring temporal consistency and reducing jitter between adjacent frames. Meanwhile, we extract the global frames of the video as prompts and guide the model to obtain information other than the current video clip using cross-attention. We also introduce a hybrid coarse-to-fine inference pipeline to alleviate the artifact accumulation problem. The existing coarse-to-fine pipeline only uses the infilling strategy, which brings degradation because the time interval of the sparse frames is too large. Our pipeline benefits from bidirectional learning of the mask modeling and thus can employ a hybrid strategy of infilling and interpolation when generating sparse frames. Experiments show that our method achieves state-of-the-art results in video outpainting tasks. More results are provided at our https://fanfanda.github.io/M3DDM/.

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by 25-75\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around 6-8times better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with 32times fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

Denoising diffusion probabilistic models have transformed image generation with their impressive fidelity and diversity. We show that they also excel in estimating optical flow and monocular depth, surprisingly, without task-specific architectures and loss functions that are predominant for these tasks. Compared to the point estimates of conventional regression-based methods, diffusion models also enable Monte Carlo inference, e.g., capturing uncertainty and ambiguity in flow and depth. With self-supervised pre-training, the combined use of synthetic and real data for supervised training, and technical innovations (infilling and step-unrolled denoising diffusion training) to handle noisy-incomplete training data, and a simple form of coarse-to-fine refinement, one can train state-of-the-art diffusion models for depth and optical flow estimation. Extensive experiments focus on quantitative performance against benchmarks, ablations, and the model's ability to capture uncertainty and multimodality, and impute missing values. Our model, DDVM (Denoising Diffusion Vision Model), obtains a state-of-the-art relative depth error of 0.074 on the indoor NYU benchmark and an Fl-all outlier rate of 3.26\% on the KITTI optical flow benchmark, about 25\% better than the best published method. For an overview see https://diffusion-vision.github.io.

Recent advances in diffusion models have successfully enabled text-guided image inpainting. While it seems straightforward to extend such editing capability into video domain, there has been fewer works regarding text-guided video inpainting. Given a video, a masked region at its initial frame, and an editing prompt, it requires a model to do infilling at each frame following the editing guidance while keeping the out-of-mask region intact. There are three main challenges in text-guided video inpainting: (i) temporal consistency of the edited video, (ii) supporting different inpainting types at different structural fidelity level, and (iii) dealing with variable video length. To address these challenges, we introduce Any-Length Video Inpainting with Diffusion Model, dubbed as AVID. At its core, our model is equipped with effective motion modules and adjustable structure guidance, for fixed-length video inpainting. Building on top of that, we propose a novel Temporal MultiDiffusion sampling pipeline with an middle-frame attention guidance mechanism, facilitating the generation of videos with any desired duration. Our comprehensive experiments show our model can robustly deal with various inpainting types at different video duration range, with high quality. More visualization results is made publicly available at https://zhang-zx.github.io/AVID/ .

Historically, LLMs have been trained using either autoregressive (AR) or masked language modeling (MLM) objectives, with AR models gaining dominance in recent years. However, AR models are inherently incapable of masked infilling, which is the ability to predict masked tokens between past and future context. In contrast, MLM models suffer from intrinsic computational inefficiencies during both training and inference that hinder their scalability. This work introduces MARIA (Masked and Autoregressive Infilling Architecture), a novel approach that leverages the strengths of both paradigms to achieve state-of-the-art masked infilling performance. MARIA combines a pre-trained MLM and AR model by training a linear decoder that takes their concatenated hidden states as input. This minimal modification enables the AR model to perform infilling while retaining its inherent advantages in terms of faster inference with KV caching. Our results demonstrate that MARIA significantly outperforms existing methods, namely discrete diffusion models, on masked infilling tasks.

We propose RoHM, an approach for robust 3D human motion reconstruction from monocular RGB(-D) videos in the presence of noise and occlusions. Most previous approaches either train neural networks to directly regress motion in 3D or learn data-driven motion priors and combine them with optimization at test time. The former do not recover globally coherent motion and fail under occlusions; the latter are time-consuming, prone to local minima, and require manual tuning. To overcome these shortcomings, we exploit the iterative, denoising nature of diffusion models. RoHM is a novel diffusion-based motion model that, conditioned on noisy and occluded input data, reconstructs complete, plausible motions in consistent global coordinates. Given the complexity of the problem -- requiring one to address different tasks (denoising and infilling) in different solution spaces (local and global motion) -- we decompose it into two sub-tasks and learn two models, one for global trajectory and one for local motion. To capture the correlations between the two, we then introduce a novel conditioning module, combining it with an iterative inference scheme. We apply RoHM to a variety of tasks -- from motion reconstruction and denoising to spatial and temporal infilling. Extensive experiments on three popular datasets show that our method outperforms state-of-the-art approaches qualitatively and quantitatively, while being faster at test time. The code will be available at https://sanweiliti.github.io/ROHM/ROHM.html.

Modern Vision-Language Models (VLMs) can solve a wide range of tasks requiring visual reasoning. In real-world scenarios, desirable properties for VLMs include fast inference and controllable generation (e.g., constraining outputs to adhere to a desired format). However, existing autoregressive (AR) VLMs like LLaVA struggle in these aspects. Discrete diffusion models (DMs) offer a promising alternative, enabling parallel decoding for faster inference and bidirectional context for controllable generation through text-infilling. While effective in language-only settings, DMs' potential for multimodal tasks is underexplored. We introduce LaViDa, a family of VLMs built on DMs. We build LaViDa by equipping DMs with a vision encoder and jointly fine-tune the combined parts for multimodal instruction following. To address challenges encountered, LaViDa incorporates novel techniques such as complementary masking for effective training, prefix KV cache for efficient inference, and timestep shifting for high-quality sampling. Experiments show that LaViDa achieves competitive or superior performance to AR VLMs on multi-modal benchmarks such as MMMU, while offering unique advantages of DMs, including flexible speed-quality tradeoff, controllability, and bidirectional reasoning. On COCO captioning, LaViDa surpasses Open-LLaVa-Next-8B by +4.1 CIDEr with 1.92x speedup. On bidirectional tasks, it achieves +59% improvement on Constrained Poem Completion. These results demonstrate LaViDa as a strong alternative to AR VLMs. Code and models will be released in the camera-ready version.

We introduce the Glauber Generative Model (GGM), a new class of discrete diffusion models, to obtain new samples from a distribution given samples from a discrete space. GGM deploys a discrete Markov chain called the heat bath dynamics (or the Glauber dynamics) to denoise a sequence of noisy tokens to a sample from a joint distribution of discrete tokens. Our novel conceptual framework provides an exact reduction of the task of learning the denoising Markov chain to solving a class of binary classification tasks. More specifically, the model learns to classify a given token in a noisy sequence as signal or noise. In contrast, prior works on discrete diffusion models either solve regression problems to learn importance ratios, or minimize loss functions given by variational approximations. We apply GGM to language modeling and image generation, where images are discretized using image tokenizers like VQGANs. We show that it outperforms existing discrete diffusion models in language generation, and demonstrates strong performance for image generation without using dataset-specific image tokenizers. We also show that our model is capable of performing well in zero-shot control settings like text and image infilling.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each task. Most inverse tasks can be formulated as inferring a posterior distribution over data (e.g., a full image) given a measurement (e.g., a masked image). This is however challenging in diffusion models since the nonlinear and iterative nature of the diffusion process renders the posterior intractable. To cope with this challenge, we propose a variational approach that by design seeks to approximate the true posterior distribution. We show that our approach naturally leads to regularization by denoising diffusion process (RED-Diff) where denoisers at different timesteps concurrently impose different structural constraints over the image. To gauge the contribution of denoisers from different timesteps, we propose a weighting mechanism based on signal-to-noise-ratio (SNR). Our approach provides a new variational perspective for solving inverse problems with diffusion models, allowing us to formulate sampling as stochastic optimization, where one can simply apply off-the-shelf solvers with lightweight iterates. Our experiments for image restoration tasks such as inpainting and superresolution demonstrate the strengths of our method compared with state-of-the-art sampling-based diffusion models.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers, acting as the prior of the distribution, while the information of the forward model can be granted at the sampling stage. Nonetheless, as the generative process remains in the same high dimensional (i.e. identical to data dimension) space, the models have not been extended to 3D inverse problems due to the extremely high memory and computational cost. In this paper, we combine the ideas from the conventional model-based iterative reconstruction with the modern diffusion models, which leads to a highly effective method for solving 3D medical image reconstruction tasks such as sparse-view tomography, limited angle tomography, compressed sensing MRI from pre-trained 2D diffusion models. In essence, we propose to augment the 2D diffusion prior with a model-based prior in the remaining direction at test time, such that one can achieve coherent reconstructions across all dimensions. Our method can be run in a single commodity GPU, and establishes the new state-of-the-art, showing that the proposed method can perform reconstructions of high fidelity and accuracy even in the most extreme cases (e.g. 2-view 3D tomography). We further reveal that the generalization capacity of the proposed method is surprisingly high, and can be used to reconstruct volumes that are entirely different from the training dataset.

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we uncover a vexing propensity of diffusion models: they frequently exhibit the infinite Lipschitz near the zero point of timesteps. This poses a threat to the stability and accuracy of the diffusion process, which relies on integral operations. We provide a comprehensive evaluation of the issue from both theoretical and empirical perspectives. To address this challenge, we propose a novel approach, dubbed E-TSDM, which eliminates the Lipschitz singularity of the diffusion model near zero. Remarkably, our technique yields a substantial improvement in performance, e.g., on the high-resolution FFHQ dataset (256times256). Moreover, as a byproduct of our method, we manage to achieve a dramatic reduction in the Frechet Inception Distance of other acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. We conduct extensive experiments on diverse datasets to validate our theory and method. Our work not only advances the understanding of the general diffusion process, but also provides insights for the design of diffusion models.

In the task of reference-based image inpainting, an additional reference image is provided to restore a damaged target image to its original state. The advancement of diffusion models, particularly Stable Diffusion, allows for simple formulations in this task. However, existing diffusion-based methods often lack explicit constraints on the correlation between the reference and damaged images, resulting in lower faithfulness to the reference images in the inpainting results. In this work, we propose CorrFill, a training-free module designed to enhance the awareness of geometric correlations between the reference and target images. This enhancement is achieved by guiding the inpainting process with correspondence constraints estimated during inpainting, utilizing attention masking in self-attention layers and an objective function to update the input tensor according to the constraints. Experimental results demonstrate that CorrFill significantly enhances the performance of multiple baseline diffusion-based methods, including state-of-the-art approaches, by emphasizing faithfulness to the reference images.

Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality images by mapping noise to a data distribution. However, recent findings suggest that image likelihood does not align with perceptual quality: high-likelihood samples tend to be smooth, while lower-likelihood ones are more detailed. Controlling sample density is thus crucial for balancing realism and detail. In this paper, we analyze an existing technique, Prior Guidance, which scales the latent code to influence image detail. We introduce score alignment, a condition that explains why this method works and show that it can be tractably checked for any continuous normalizing flow model. We then propose Density Guidance, a principled modification of the generative ODE that enables exact log-density control during sampling. Finally, we extend Density Guidance to stochastic sampling, ensuring precise log-density control while allowing controlled variation in structure or fine details. Our experiments demonstrate that these techniques provide fine-grained control over image detail without compromising sample quality.

Denoising diffusion models, a class of generative models, have garnered immense interest lately in various deep-learning problems. A diffusion probabilistic model defines a forward diffusion stage where the input data is gradually perturbed over several steps by adding Gaussian noise and then learns to reverse the diffusion process to retrieve the desired noise-free data from noisy data samples. Diffusion models are widely appreciated for their strong mode coverage and quality of the generated samples despite their known computational burdens. Capitalizing on the advances in computer vision, the field of medical imaging has also observed a growing interest in diffusion models. To help the researcher navigate this profusion, this survey intends to provide a comprehensive overview of diffusion models in the discipline of medical image analysis. Specifically, we introduce the solid theoretical foundation and fundamental concepts behind diffusion models and the three generic diffusion modelling frameworks: diffusion probabilistic models, noise-conditioned score networks, and stochastic differential equations. Then, we provide a systematic taxonomy of diffusion models in the medical domain and propose a multi-perspective categorization based on their application, imaging modality, organ of interest, and algorithms. To this end, we cover extensive applications of diffusion models in the medical domain. Furthermore, we emphasize the practical use case of some selected approaches, and then we discuss the limitations of the diffusion models in the medical domain and propose several directions to fulfill the demands of this field. Finally, we gather the overviewed studies with their available open-source implementations at https://github.com/amirhossein-kz/Awesome-Diffusion-Models-in-Medical-Imaging.

Generating background scenes for salient objects plays a crucial role across various domains including creative design and e-commerce, as it enhances the presentation and context of subjects by integrating them into tailored environments. Background generation can be framed as a task of text-conditioned outpainting, where the goal is to extend image content beyond a salient object's boundaries on a blank background. Although popular diffusion models for text-guided inpainting can also be used for outpainting by mask inversion, they are trained to fill in missing parts of an image rather than to place an object into a scene. Consequently, when used for background creation, inpainting models frequently extend the salient object's boundaries and thereby change the object's identity, which is a phenomenon we call "object expansion." This paper introduces a model for adapting inpainting diffusion models to the salient object outpainting task using Stable Diffusion and ControlNet architectures. We present a series of qualitative and quantitative results across models and datasets, including a newly proposed metric to measure object expansion that does not require any human labeling. Compared to Stable Diffusion 2.0 Inpainting, our proposed approach reduces object expansion by 3.6x on average with no degradation in standard visual metrics across multiple datasets.

Masked (or absorbing) diffusion is actively explored as an alternative to autoregressive models for generative modeling of discrete data. However, existing work in this area has been hindered by unnecessarily complex model formulations and unclear relationships between different perspectives, leading to suboptimal parameterization, training objectives, and ad hoc adjustments to counteract these issues. In this work, we aim to provide a simple and general framework that unlocks the full potential of masked diffusion models. We show that the continuous-time variational objective of masked diffusion models is a simple weighted integral of cross-entropy losses. Our framework also enables training generalized masked diffusion models with state-dependent masking schedules. When evaluated by perplexity, our models trained on OpenWebText surpass prior diffusion language models at GPT-2 scale and demonstrate superior performance on 4 out of 5 zero-shot language modeling tasks. Furthermore, our models vastly outperform previous discrete diffusion models on pixel-level image modeling, achieving 2.78~(CIFAR-10) and 3.42 (ImageNet 64times64) bits per dimension that are comparable or better than autoregressive models of similar sizes.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview of the rapidly expanding body of work on diffusion models, categorizing the research into three key areas: efficient sampling, improved likelihood estimation, and handling data with special structures. We also discuss the potential for combining diffusion models with other generative models for enhanced results. We further review the wide-ranging applications of diffusion models in fields spanning from computer vision, natural language generation, temporal data modeling, to interdisciplinary applications in other scientific disciplines. This survey aims to provide a contextualized, in-depth look at the state of diffusion models, identifying the key areas of focus and pointing to potential areas for further exploration. Github: https://github.com/YangLing0818/Diffusion-Models-Papers-Survey-Taxonomy.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.

Inpainting focuses on filling missing or corrupted regions of an image to blend seamlessly with its surrounding content and style. While conditional diffusion models have proven effective for text-guided inpainting, we introduce the novel task of multi-mask inpainting, where multiple regions are simultaneously inpainted using distinct prompts. Furthermore, we design a fine-tuning procedure for multimodal LLMs, such as LLaVA, to generate multi-mask prompts automatically using corrupted images as inputs. These models can generate helpful and detailed prompt suggestions for filling the masked regions. The generated prompts are then fed to Stable Diffusion, which is fine-tuned for the multi-mask inpainting problem using rectified cross-attention, enforcing prompts onto their designated regions for filling. Experiments on digitized paintings from WikiArt and the Densely Captioned Images dataset demonstrate that our pipeline delivers creative and accurate inpainting results. Our code, data, and trained models are available at https://cilabuniba.github.io/i-dream-my-painting.

Diffusion models have achieved remarkable success in the domain of text-guided image generation and, more recently, in text-guided image editing. A commonly adopted strategy for editing real images involves inverting the diffusion process to obtain a noisy representation of the original image, which is then denoised to achieve the desired edits. However, current methods for diffusion inversion often struggle to produce edits that are both faithful to the specified text prompt and closely resemble the source image. To overcome these limitations, we introduce a novel and adaptable diffusion inversion technique for real image editing, which is grounded in a theoretical analysis of the role of eta in the DDIM sampling equation for enhanced editability. By designing a universal diffusion inversion method with a time- and region-dependent eta function, we enable flexible control over the editing extent. Through a comprehensive series of quantitative and qualitative assessments, involving a comparison with a broad array of recent methods, we demonstrate the superiority of our approach. Our method not only sets a new benchmark in the field but also significantly outperforms existing strategies.

Diffusion models have become a popular approach for image generation and reconstruction due to their numerous advantages. However, most diffusion-based inverse problem-solving methods only deal with 2D images, and even recently published 3D methods do not fully exploit the 3D distribution prior. To address this, we propose a novel approach using two perpendicular pre-trained 2D diffusion models to solve the 3D inverse problem. By modeling the 3D data distribution as a product of 2D distributions sliced in different directions, our method effectively addresses the curse of dimensionality. Our experimental results demonstrate that our method is highly effective for 3D medical image reconstruction tasks, including MRI Z-axis super-resolution, compressed sensing MRI, and sparse-view CT. Our method can generate high-quality voxel volumes suitable for medical applications.

Diffusion models (DMs) have established themselves as the state-of-the-art generative modeling approach in the visual domain and beyond. A crucial drawback of DMs is their slow sampling speed, relying on many sequential function evaluations through large neural networks. Sampling from DMs can be seen as solving a differential equation through a discretized set of noise levels known as the sampling schedule. While past works primarily focused on deriving efficient solvers, little attention has been given to finding optimal sampling schedules, and the entire literature relies on hand-crafted heuristics. In this work, for the first time, we propose a general and principled approach to optimizing the sampling schedules of DMs for high-quality outputs, called Align Your Steps. We leverage methods from stochastic calculus and find optimal schedules specific to different solvers, trained DMs and datasets. We evaluate our novel approach on several image, video as well as 2D toy data synthesis benchmarks, using a variety of different samplers, and observe that our optimized schedules outperform previous hand-crafted schedules in almost all experiments. Our method demonstrates the untapped potential of sampling schedule optimization, especially in the few-step synthesis regime.

Diffusion models have achieved remarkable success in image generation, with applications broadening across various domains. Inpainting is one such application that can benefit significantly from diffusion models. Existing methods either hijack the reverse process of a pretrained diffusion model or cast the problem into a larger framework, \ie, conditioned generation. However, these approaches often require nested loops in the generation process or additional components for conditioning. In this paper, we present region-aware diffusion models (RAD) for inpainting with a simple yet effective reformulation of the vanilla diffusion models. RAD utilizes a different noise schedule for each pixel, which allows local regions to be generated asynchronously while considering the global image context. A plain reverse process requires no additional components, enabling RAD to achieve inference time up to 100 times faster than the state-of-the-art approaches. Moreover, we employ low-rank adaptation (LoRA) to fine-tune RAD based on other pretrained diffusion models, reducing computational burdens in training as well. Experiments demonstrated that RAD provides state-of-the-art results both qualitatively and quantitatively, on the FFHQ, LSUN Bedroom, and ImageNet datasets.

Diffusion models are a new class of generative models, and have dramatically promoted image generation with unprecedented quality and diversity. Existing diffusion models mainly try to reconstruct input image from a corrupted one with a pixel-wise or feature-wise constraint along spatial axes. However, such point-based reconstruction may fail to make each predicted pixel/feature fully preserve its neighborhood context, impairing diffusion-based image synthesis. As a powerful source of automatic supervisory signal, context has been well studied for learning representations. Inspired by this, we for the first time propose ConPreDiff to improve diffusion-based image synthesis with context prediction. We explicitly reinforce each point to predict its neighborhood context (i.e., multi-stride features/tokens/pixels) with a context decoder at the end of diffusion denoising blocks in training stage, and remove the decoder for inference. In this way, each point can better reconstruct itself by preserving its semantic connections with neighborhood context. This new paradigm of ConPreDiff can generalize to arbitrary discrete and continuous diffusion backbones without introducing extra parameters in sampling procedure. Extensive experiments are conducted on unconditional image generation, text-to-image generation and image inpainting tasks. Our ConPreDiff consistently outperforms previous methods and achieves a new SOTA text-to-image generation results on MS-COCO, with a zero-shot FID score of 6.21.

Diffusion models are the current state-of-the-art in image generation, synthesizing high-quality images by breaking down the generation process into many fine-grained denoising steps. Despite their good performance, diffusion models are computationally expensive, requiring many neural function evaluations (NFEs). In this work, we propose an anytime diffusion-based method that can generate viable images when stopped at arbitrary times before completion. Using existing pretrained diffusion models, we show that the generation scheme can be recomposed as two nested diffusion processes, enabling fast iterative refinement of a generated image. We use this Nested Diffusion approach to peek into the generation process and enable flexible scheduling based on the instantaneous preference of the user. In experiments on ImageNet and Stable Diffusion-based text-to-image generation, we show, both qualitatively and quantitatively, that our method's intermediate generation quality greatly exceeds that of the original diffusion model, while the final slow generation result remains comparable.

Diffusion models (DMs) demonstrate potent image generation capabilities in various generative modeling tasks. Nevertheless, their primary limitation lies in slow sampling speed, requiring hundreds or thousands of sequential function evaluations through large neural networks to generate high-quality images. Sampling from DMs can be seen alternatively as solving corresponding stochastic differential equations (SDEs) or ordinary differential equations (ODEs). In this work, we formulate the sampling process as an extended reverse-time SDE (ER SDE), unifying prior explorations into ODEs and SDEs. Leveraging the semi-linear structure of ER SDE solutions, we offer exact solutions and arbitrarily high-order approximate solutions for VP SDE and VE SDE, respectively. Based on the solution space of the ER SDE, we yield mathematical insights elucidating the superior performance of ODE solvers over SDE solvers in terms of fast sampling. Additionally, we unveil that VP SDE solvers stand on par with their VE SDE counterparts. Finally, we devise fast and training-free samplers, ER-SDE-Solvers, achieving state-of-the-art performance across all stochastic samplers. Experimental results demonstrate achieving 3.45 FID in 20 function evaluations and 2.24 FID in 50 function evaluations on the ImageNet 64times64 dataset.

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical solvers. Most existing forward or inverse PDE approaches perform poorly when the observations on the data or the underlying coefficients are incomplete, which is a common assumption for real-world measurements. In this work, we propose DiffusionPDE that can simultaneously fill in the missing information and solve a PDE by modeling the joint distribution of the solution and coefficient spaces. We show that the learned generative priors lead to a versatile framework for accurately solving a wide range of PDEs under partial observation, significantly outperforming the state-of-the-art methods for both forward and inverse directions.

Denoising diffusion models have emerged as a powerful tool for various image generation and editing tasks, facilitating the synthesis of visual content in an unconditional or input-conditional manner. The core idea behind them is learning to reverse the process of gradually adding noise to images, allowing them to generate high-quality samples from a complex distribution. In this survey, we provide an exhaustive overview of existing methods using diffusion models for image editing, covering both theoretical and practical aspects in the field. We delve into a thorough analysis and categorization of these works from multiple perspectives, including learning strategies, user-input conditions, and the array of specific editing tasks that can be accomplished. In addition, we pay special attention to image inpainting and outpainting, and explore both earlier traditional context-driven and current multimodal conditional methods, offering a comprehensive analysis of their methodologies. To further evaluate the performance of text-guided image editing algorithms, we propose a systematic benchmark, EditEval, featuring an innovative metric, LMM Score. Finally, we address current limitations and envision some potential directions for future research. The accompanying repository is released at https://github.com/SiatMMLab/Awesome-Diffusion-Model-Based-Image-Editing-Methods.

Recent video inpainting algorithms integrate flow-based pixel propagation with transformer-based generation to leverage optical flow for restoring textures and objects using information from neighboring frames, while completing masked regions through visual Transformers. However, these approaches often encounter blurring and temporal inconsistencies when dealing with large masks, highlighting the need for models with enhanced generative capabilities. Recently, diffusion models have emerged as a prominent technique in image and video generation due to their impressive performance. In this paper, we introduce DiffuEraser, a video inpainting model based on stable diffusion, designed to fill masked regions with greater details and more coherent structures. We incorporate prior information to provide initialization and weak conditioning,which helps mitigate noisy artifacts and suppress hallucinations. Additionally, to improve temporal consistency during long-sequence inference, we expand the temporal receptive fields of both the prior model and DiffuEraser, and further enhance consistency by leveraging the temporal smoothing property of Video Diffusion Models. Experimental results demonstrate that our proposed method outperforms state-of-the-art techniques in both content completeness and temporal consistency while maintaining acceptable efficiency.

Diffusion models have become the go-to method for large-scale generative models in real-world applications. These applications often involve data distributions confined within bounded domains, typically requiring ad-hoc thresholding techniques for boundary enforcement. Reflected diffusion models (Lou23) aim to enhance generalizability by generating the data distribution through a backward process governed by reflected Brownian motion. However, reflected diffusion models may not easily adapt to diverse domains without the derivation of proper diffeomorphic mappings and do not guarantee optimal transport properties. To overcome these limitations, we introduce the Reflected Schrodinger Bridge algorithm: an entropy-regularized optimal transport approach tailored for generating data within diverse bounded domains. We derive elegant reflected forward-backward stochastic differential equations with Neumann and Robin boundary conditions, extend divergence-based likelihood training to bounded domains, and explore natural connections to entropic optimal transport for the study of approximate linear convergence - a valuable insight for practical training. Our algorithm yields robust generative modeling in diverse domains, and its scalability is demonstrated in real-world constrained generative modeling through standard image benchmarks.

Denoising diffusion models (DDMs) have recently attracted increasing attention by showing impressive synthesis quality. DDMs are built on a diffusion process that pushes data to the noise distribution and the models learn to denoise. In this paper, we establish the interpretation of DDMs in terms of image restoration (IR). Integrating IR literature allows us to use an alternative objective and diverse forward processes, not confining to the diffusion process. By imposing prior knowledge on the loss function grounded on MAP-based estimation, we eliminate the need for the expensive sampling of DDMs. Also, we propose a multi-scale training, which improves the performance compared to the diffusion process, by taking advantage of the flexibility of the forward process. Experimental results demonstrate that our model improves the quality and efficiency of both training and inference. Furthermore, we show the applicability of our model to inverse problems. We believe that our framework paves the way for designing a new type of flexible general generative model.

We propose a new method for solving imaging inverse problems using text-to-image latent diffusion models as general priors. Existing methods using latent diffusion models for inverse problems typically rely on simple null text prompts, which can lead to suboptimal performance. To address this limitation, we introduce a method for prompt tuning, which jointly optimizes the text embedding on-the-fly while running the reverse diffusion process. This allows us to generate images that are more faithful to the diffusion prior. In addition, we propose a method to keep the evolution of latent variables within the range space of the encoder, by projection. This helps to reduce image artifacts, a major problem when using latent diffusion models instead of pixel-based diffusion models. Our combined method, called P2L, outperforms both image- and latent-diffusion model-based inverse problem solvers on a variety of tasks, such as super-resolution, deblurring, and inpainting.

By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a guiding mechanism to control the image generation process without retraining. However, since these models typically operate directly in pixel space, optimization of powerful DMs often consumes hundreds of GPU days and inference is expensive due to sequential evaluations. To enable DM training on limited computational resources while retaining their quality and flexibility, we apply them in the latent space of powerful pretrained autoencoders. In contrast to previous work, training diffusion models on such a representation allows for the first time to reach a near-optimal point between complexity reduction and detail preservation, greatly boosting visual fidelity. By introducing cross-attention layers into the model architecture, we turn diffusion models into powerful and flexible generators for general conditioning inputs such as text or bounding boxes and high-resolution synthesis becomes possible in a convolutional manner. Our latent diffusion models (LDMs) achieve a new state of the art for image inpainting and highly competitive performance on various tasks, including unconditional image generation, semantic scene synthesis, and super-resolution, while significantly reducing computational requirements compared to pixel-based DMs. Code is available at https://github.com/CompVis/latent-diffusion .

As online shopping is growing, the ability for buyers to virtually visualize products in their settings-a phenomenon we define as "Virtual Try-All"-has become crucial. Recent diffusion models inherently contain a world model, rendering them suitable for this task within an inpainting context. However, traditional image-conditioned diffusion models often fail to capture the fine-grained details of products. In contrast, personalization-driven models such as DreamPaint are good at preserving the item's details but they are not optimized for real-time applications. We present "Diffuse to Choose," a novel diffusion-based image-conditioned inpainting model that efficiently balances fast inference with the retention of high-fidelity details in a given reference item while ensuring accurate semantic manipulations in the given scene content. Our approach is based on incorporating fine-grained features from the reference image directly into the latent feature maps of the main diffusion model, alongside with a perceptual loss to further preserve the reference item's details. We conduct extensive testing on both in-house and publicly available datasets, and show that Diffuse to Choose is superior to existing zero-shot diffusion inpainting methods as well as few-shot diffusion personalization algorithms like DreamPaint.

Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. DMs work by constructing a Stochastic Differential Equation (SDE) in the input space (ie, position space), and using a neural network to reverse it. In this work, we introduce a novel generative modeling framework grounded in phase space dynamics, where a phase space is defined as {an augmented space encompassing both position and velocity.} Leveraging insights from Stochastic Optimal Control, we construct a path measure in the phase space that enables efficient sampling. {In contrast to DMs, our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.} This early prediction sets the stage for efficient data generation by leveraging additional velocity information along the trajectory. On standard image generation benchmarks, our model yields favorable performance over baselines in the regime of small Number of Function Evaluations (NFEs). Furthermore, our approach rivals the performance of diffusion models equipped with efficient sampling techniques, underscoring its potential as a new tool generative modeling.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Diffusion models (DMs) excel in photorealism, image editing, and solving inverse problems, aided by classifier-free guidance and image inversion techniques. However, rectified flow models (RFMs) remain underexplored for these tasks. Existing DM-based methods often require additional training, lack generalization to pretrained latent models, underperform, and demand significant computational resources due to extensive backpropagation through ODE solvers and inversion processes. In this work, we first develop a theoretical and empirical understanding of the vector field dynamics of RFMs in efficiently guiding the denoising trajectory. Our findings reveal that we can navigate the vector field in a deterministic and gradient-free manner. Utilizing this property, we propose FlowChef, which leverages the vector field to steer the denoising trajectory for controlled image generation tasks, facilitated by gradient skipping. FlowChef is a unified framework for controlled image generation that, for the first time, simultaneously addresses classifier guidance, linear inverse problems, and image editing without the need for extra training, inversion, or intensive backpropagation. Finally, we perform extensive evaluations and show that FlowChef significantly outperforms baselines in terms of performance, memory, and time requirements, achieving new state-of-the-art results. Project Page: https://flowchef.github.io.

We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion model trained on a novel benchmark dataset comprising 1,000 synthetically simulated volumetric density fields. The neural diffusion model is trained on the latent codes of a novel, diffusion-friendly, monoplanar representation. The generative model is used to incorporate a tailored parametric diffusion posterior sampling technique into different reconstruction tasks. A physically-based differentiable volume renderer is employed to provide gradients with respect to light transport in the latent space. This stands in contrast to classic NeRF approaches and makes the reconstructions better aligned with observed data. Through various experiments, we demonstrate single-view reconstruction of volumetric clouds at a previously unattainable quality.

Diffusion models are well known for their ability to generate a high-fidelity image for an input prompt through an iterative denoising process. Unfortunately, the high fidelity also comes at a high computational cost due the inherently sequential generative process. In this work, we seek to optimally balance quality and computational cost, and propose a framework to allow the amount of computation to vary for each prompt, depending on its complexity. Each prompt is automatically routed to the most appropriate text-to-image generation function, which may correspond to a distinct number of denoising steps of a diffusion model, or a disparate, independent text-to-image model. Unlike uniform cost reduction techniques (e.g., distillation, model quantization), our approach achieves the optimal trade-off by learning to reserve expensive choices (e.g., 100+ denoising steps) only for a few complex prompts, and employ more economical choices (e.g., small distilled model) for less sophisticated prompts. We empirically demonstrate on COCO and DiffusionDB that by learning to route to nine already-trained text-to-image models, our approach is able to deliver an average quality that is higher than that achievable by any of these models alone.

We introduce infty-Diff, a generative diffusion model which directly operates on infinite resolution data. By randomly sampling subsets of coordinates during training and learning to denoise the content at those coordinates, a continuous function is learned that allows sampling at arbitrary resolutions. In contrast to other recent infinite resolution generative models, our approach operates directly on the raw data, not requiring latent vector compression for context, using hypernetworks, nor relying on discrete components. As such, our approach achieves significantly higher sample quality, as evidenced by lower FID scores, as well as being able to effectively scale to higher resolutions than the training data while retaining detail.

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment. Although recent methods utilize pre-trained diffusion models for image reconstruction, they struggle with slow inference and restricted adaptability to CS. To tackle these challenges, this paper proposes Invertible Diffusion Models (IDM), a novel efficient, end-to-end diffusion-based CS method. IDM repurposes a large-scale diffusion sampling process as a reconstruction model, and fine-tunes it end-to-end to recover original images directly from CS measurements, moving beyond the traditional paradigm of one-step noise estimation learning. To enable such memory-intensive end-to-end fine-tuning, we propose a novel two-level invertible design to transform both (1) multi-step sampling process and (2) noise estimation U-Net in each step into invertible networks. As a result, most intermediate features are cleared during training to reduce up to 93.8% GPU memory. In addition, we develop a set of lightweight modules to inject measurements into noise estimator to further facilitate reconstruction. Experiments demonstrate that IDM outperforms existing state-of-the-art CS networks by up to 2.64dB in PSNR. Compared to the recent diffusion-based approach DDNM, our IDM achieves up to 10.09dB PSNR gain and 14.54 times faster inference. Code is available at https://github.com/Guaishou74851/IDM.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

Image inpainting, the process of restoring corrupted images, has seen significant advancements with the advent of diffusion models (DMs). Despite these advancements, current DM adaptations for inpainting, which involve modifications to the sampling strategy or the development of inpainting-specific DMs, frequently suffer from semantic inconsistencies and reduced image quality. Addressing these challenges, our work introduces a novel paradigm: the division of masked image features and noisy latent into separate branches. This division dramatically diminishes the model's learning load, facilitating a nuanced incorporation of essential masked image information in a hierarchical fashion. Herein, we present BrushNet, a novel plug-and-play dual-branch model engineered to embed pixel-level masked image features into any pre-trained DM, guaranteeing coherent and enhanced image inpainting outcomes. Additionally, we introduce BrushData and BrushBench to facilitate segmentation-based inpainting training and performance assessment. Our extensive experimental analysis demonstrates BrushNet's superior performance over existing models across seven key metrics, including image quality, mask region preservation, and textual coherence.

Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative trajectories, and results in costly inference for diffusion models. To address these limitations, we introduce Neural Flow Diffusion Models (NFDM), a novel framework that enhances diffusion models by supporting a broader range of forward processes beyond the fixed linear Gaussian. We also propose a novel parameterization technique for learning the forward process. Our framework provides an end-to-end, simulation-free optimization objective, effectively minimizing a variational upper bound on the negative log-likelihood. Experimental results demonstrate NFDM's strong performance, evidenced by state-of-the-art likelihood estimation. Furthermore, we investigate NFDM's capacity for learning generative dynamics with specific characteristics, such as deterministic straight lines trajectories. This exploration underscores NFDM's versatility and its potential for a wide range of applications.

A popular approach to sample a diffusion-based generative model is to solve an ordinary differential equation (ODE). In existing samplers, the coefficients of the ODE solvers are pre-determined by the ODE formulation, the reverse discrete timesteps, and the employed ODE methods. In this paper, we consider accelerating several popular ODE-based sampling processes (including EDM, DDIM, and DPM-Solver) by optimizing certain coefficients via improved integration approximation (IIA). We propose to minimize, for each time step, a mean squared error (MSE) function with respect to the selected coefficients. The MSE is constructed by applying the original ODE solver for a set of fine-grained timesteps, which in principle provides a more accurate integration approximation in predicting the next diffusion state. The proposed IIA technique does not require any change of a pre-trained model, and only introduces a very small computational overhead for solving a number of quadratic optimization problems. Extensive experiments show that considerably better FID scores can be achieved by using IIA-EDM, IIA-DDIM, and IIA-DPM-Solver than the original counterparts when the neural function evaluation (NFE) is small (i.e., less than 25).

Diffusion models (DMs) have gained prominence due to their ability to generate high-quality, varied images, with recent advancements in text-to-image generation. The research focus is now shifting towards the controllability of DMs. A significant challenge within this domain is localized editing, where specific areas of an image are modified without affecting the rest of the content. This paper introduces LIME for localized image editing in diffusion models that do not require user-specified regions of interest (RoI) or additional text input. Our method employs features from pre-trained methods and a simple clustering technique to obtain precise semantic segmentation maps. Then, by leveraging cross-attention maps, it refines these segments for localized edits. Finally, we propose a novel cross-attention regularization technique that penalizes unrelated cross-attention scores in the RoI during the denoising steps, ensuring localized edits. Our approach, without re-training and fine-tuning, consistently improves the performance of existing methods in various editing benchmarks.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

We present a dynamic model in which the weights are conditioned on an input sample x and are learned to match those that would be obtained by finetuning a base model on x and its label y. This mapping between an input sample and network weights is approximated by a denoising diffusion model. The diffusion model we employ focuses on modifying a single layer of the base model and is conditioned on the input, activations, and output of this layer. Since the diffusion model is stochastic in nature, multiple initializations generate different networks, forming an ensemble, which leads to further improvements. Our experiments demonstrate the wide applicability of the method for image classification, 3D reconstruction, tabular data, speech separation, and natural language processing. Our code is available at https://github.com/ShaharLutatiPersonal/OCD

Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the intrinsic mutual interference among image regions contradicts the need for practical downstream application scenarios where the preservation of low-level pixel information from given conditioning is desired (e.g., customization tasks like personalized generation and inpainting based on a user-provided single image). In this work, we investigate the diffusion (physics) in diffusion (machine learning) properties and propose our Cyclic One-Way Diffusion (COW) method to control the direction of diffusion phenomenon given a pre-trained frozen diffusion model for versatile customization application scenarios, where the low-level pixel information from the conditioning needs to be preserved. Notably, unlike most current methods that incorporate additional conditions by fine-tuning the base text-to-image diffusion model or learning auxiliary networks, our method provides a novel perspective to understand the task needs and is applicable to a wider range of customization scenarios in a learning-free manner. Extensive experiment results show that our proposed COW can achieve more flexible customization based on strict visual conditions in different application settings. Project page: https://wangruoyu02.github.io/cow.github.io/.

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.

Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. To resolve this, we introduce the Logistic Schedule, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness.

Current diffusion-based image restoration methods feed degraded input images as conditions into the noise estimation network. However, interpreting this diffusion process is challenging since it essentially generates the target image from the noise. To establish a unified and more interpretable model for image generation and restoration, we propose residual denoising diffusion models (RDDM). In contrast to existing diffusion models (e.g., DDPM or DDIM) that focus solely on noise estimation, our RDDM predicts residuals to represent directional diffusion from the target domain to the input domain, while concurrently estimating noise to account for random perturbations in the diffusion process. The introduction of residuals allows us to redefine the forward diffusion process, wherein the target image progressively diffuses into a purely noisy image or a noise-carrying input image, thus unifying image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, with native support for conditional inputs, our RDDM enables a generic UNet, trained with only an ell _1 loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

We present Diffusion Model Patching (DMP), a simple method to boost the performance of pre-trained diffusion models that have already reached convergence, with a negligible increase in parameters. DMP inserts a small, learnable set of prompts into the model's input space while keeping the original model frozen. The effectiveness of DMP is not merely due to the addition of parameters but stems from its dynamic gating mechanism, which selects and combines a subset of learnable prompts at every step of the generative process (e.g., reverse denoising steps). This strategy, which we term "mixture-of-prompts", enables the model to draw on the distinct expertise of each prompt, essentially "patching" the model's functionality at every step with minimal yet specialized parameters. Uniquely, DMP enhances the model by further training on the same dataset on which it was originally trained, even in a scenario where significant improvements are typically not expected due to model convergence. Experiments show that DMP significantly enhances the converged FID of DiT-L/2 on FFHQ 256x256 by 10.38%, achieved with only a 1.43% parameter increase and 50K additional training iterations.

Distillation techniques have substantially improved the sampling speed of diffusion models, allowing of the generation within only one step or a few steps. However, these distillation methods require extensive training for each dataset, sampler, and network, which limits their practical applicability. To address this limitation, we propose a straightforward distillation approach, Distilled-ODE solvers (D-ODE solvers), that optimizes the ODE solver rather than training the denoising network. D-ODE solvers are formulated by simply applying a single parameter adjustment to existing ODE solvers. Subsequently, D-ODE solvers with smaller steps are optimized by ODE solvers with larger steps through distillation over a batch of samples. Our comprehensive experiments indicate that D-ODE solvers outperform existing ODE solvers, including DDIM, PNDM, DPM-Solver, DEIS, and EDM, especially when generating samples with fewer steps. Our method incur negligible computational overhead compared to previous distillation techniques, enabling simple and rapid integration with previous samplers. Qualitative analysis further shows that D-ODE solvers enhance image quality while preserving the sampling trajectory of ODE solvers.

We present a method for generating video sequences with coherent motion between a pair of input key frames. We adapt a pretrained large-scale image-to-video diffusion model (originally trained to generate videos moving forward in time from a single input image) for key frame interpolation, i.e., to produce a video in between two input frames. We accomplish this adaptation through a lightweight fine-tuning technique that produces a version of the model that instead predicts videos moving backwards in time from a single input image. This model (along with the original forward-moving model) is subsequently used in a dual-directional diffusion sampling process that combines the overlapping model estimates starting from each of the two keyframes. Our experiments show that our method outperforms both existing diffusion-based methods and traditional frame interpolation techniques.

Text-to-image generative models have made remarkable advancements in generating high-quality images. However, generated images often contain undesirable artifacts or other errors due to model limitations. Existing techniques to fine-tune generated images are time-consuming (manual editing), produce poorly-integrated results (inpainting), or result in unexpected changes across the entire image (variation selection and prompt fine-tuning). In this work, we present Diffusion Brush, a Latent Diffusion Model-based (LDM) tool to efficiently fine-tune desired regions within an AI-synthesized image. Our method introduces new random noise patterns at targeted regions during the reverse diffusion process, enabling the model to efficiently make changes to the specified regions while preserving the original context for the rest of the image. We evaluate our method's usability and effectiveness through a user study with artists, comparing our technique against other state-of-the-art image inpainting techniques and editing software for fine-tuning AI-generated imagery.

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting, where generating stable and accurate rollout forecasts remains challenging, Our method, DYffusion, leverages the temporal dynamics in the data, directly coupling it with the diffusion steps in the model. We train a stochastic, time-conditioned interpolator and a forecaster network that mimic the forward and reverse processes of standard diffusion models, respectively. DYffusion naturally facilitates multi-step and long-range forecasting, allowing for highly flexible, continuous-time sampling trajectories and the ability to trade-off performance with accelerated sampling at inference time. In addition, the dynamics-informed diffusion process in DYffusion imposes a strong inductive bias and significantly improves computational efficiency compared to traditional Gaussian noise-based diffusion models. Our approach performs competitively on probabilistic forecasting of complex dynamics in sea surface temperatures, Navier-Stokes flows, and spring mesh systems.

Diffusion models (DMs) have shown remarkable capabilities in generating realistic high-quality images, audios, and videos. They benefit significantly from extensive pre-training on large-scale datasets, including web-crawled data with paired data and conditions, such as image-text and image-class pairs. Despite rigorous filtering, these pre-training datasets often inevitably contain corrupted pairs where conditions do not accurately describe the data. This paper presents the first comprehensive study on the impact of such corruption in pre-training data of DMs. We synthetically corrupt ImageNet-1K and CC3M to pre-train and evaluate over 50 conditional DMs. Our empirical findings reveal that various types of slight corruption in pre-training can significantly enhance the quality, diversity, and fidelity of the generated images across different DMs, both during pre-training and downstream adaptation stages. Theoretically, we consider a Gaussian mixture model and prove that slight corruption in the condition leads to higher entropy and a reduced 2-Wasserstein distance to the ground truth of the data distribution generated by the corruptly trained DMs. Inspired by our analysis, we propose a simple method to improve the training of DMs on practical datasets by adding condition embedding perturbations (CEP). CEP significantly improves the performance of various DMs in both pre-training and downstream tasks. We hope that our study provides new insights into understanding the data and pre-training processes of DMs.

Image editing has advanced significantly with the introduction of text-conditioned diffusion models. Despite this progress, seamlessly adding objects to images based on textual instructions without requiring user-provided input masks remains a challenge. We address this by leveraging the insight that removing objects (Inpaint) is significantly simpler than its inverse process of adding them (Paint), attributed to the utilization of segmentation mask datasets alongside inpainting models that inpaint within these masks. Capitalizing on this realization, by implementing an automated and extensive pipeline, we curate a filtered large-scale image dataset containing pairs of images and their corresponding object-removed versions. Using these pairs, we train a diffusion model to inverse the inpainting process, effectively adding objects into images. Unlike other editing datasets, ours features natural target images instead of synthetic ones; moreover, it maintains consistency between source and target by construction. Additionally, we utilize a large Vision-Language Model to provide detailed descriptions of the removed objects and a Large Language Model to convert these descriptions into diverse, natural-language instructions. We show that the trained model surpasses existing ones both qualitatively and quantitatively, and release the large-scale dataset alongside the trained models for the community.

Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

Generative models transform random noise into images; their inversion aims to transform images back to structured noise for recovery and editing. This paper addresses two key tasks: (i) inversion and (ii) editing of a real image using stochastic equivalents of rectified flow models (such as Flux). Although Diffusion Models (DMs) have recently dominated the field of generative modeling for images, their inversion presents faithfulness and editability challenges due to nonlinearities in drift and diffusion. Existing state-of-the-art DM inversion approaches rely on training of additional parameters or test-time optimization of latent variables; both are expensive in practice. Rectified Flows (RFs) offer a promising alternative to diffusion models, yet their inversion has been underexplored. We propose RF inversion using dynamic optimal control derived via a linear quadratic regulator. We prove that the resulting vector field is equivalent to a rectified stochastic differential equation. Additionally, we extend our framework to design a stochastic sampler for Flux. Our inversion method allows for state-of-the-art performance in zero-shot inversion and editing, outperforming prior works in stroke-to-image synthesis and semantic image editing, with large-scale human evaluations confirming user preference.

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities. However, applying these methods to real images necessitates the inversion of the images into the domain of the pretrained diffusion model. Achieving faithful inversion remains a challenge, particularly for more recent models trained to generate images with a small number of denoising steps. In this work, we introduce an inversion method with a high quality-to-operation ratio, enhancing reconstruction accuracy without increasing the number of operations. Building on reversing the diffusion sampling process, our method employs an iterative renoising mechanism at each inversion sampling step. This mechanism refines the approximation of a predicted point along the forward diffusion trajectory, by iteratively applying the pretrained diffusion model, and averaging these predictions. We evaluate the performance of our ReNoise technique using various sampling algorithms and models, including recent accelerated diffusion models. Through comprehensive evaluations and comparisons, we show its effectiveness in terms of both accuracy and speed. Furthermore, we confirm that our method preserves editability by demonstrating text-driven image editing on real images.

Denoising diffusion models (DDMs) have attracted attention for their exceptional generation quality and diversity. This success is largely attributed to the use of class- or text-conditional diffusion guidance methods, such as classifier and classifier-free guidance. In this paper, we present a more comprehensive perspective that goes beyond the traditional guidance methods. From this generalized perspective, we introduce novel condition- and training-free strategies to enhance the quality of generated images. As a simple solution, blur guidance improves the suitability of intermediate samples for their fine-scale information and structures, enabling diffusion models to generate higher quality samples with a moderate guidance scale. Improving upon this, Self-Attention Guidance (SAG) uses the intermediate self-attention maps of diffusion models to enhance their stability and efficacy. Specifically, SAG adversarially blurs only the regions that diffusion models attend to at each iteration and guides them accordingly. Our experimental results show that our SAG improves the performance of various diffusion models, including ADM, IDDPM, Stable Diffusion, and DiT. Moreover, combining SAG with conventional guidance methods leads to further improvement.

Standard diffusion models involve an image transform -- adding Gaussian noise -- and an image restoration operator that inverts this degradation. We observe that the generative behavior of diffusion models is not strongly dependent on the choice of image degradation, and in fact an entire family of generative models can be constructed by varying this choice. Even when using completely deterministic degradations (e.g., blur, masking, and more), the training and test-time update rules that underlie diffusion models can be easily generalized to create generative models. The success of these fully deterministic models calls into question the community's understanding of diffusion models, which relies on noise in either gradient Langevin dynamics or variational inference, and paves the way for generalized diffusion models that invert arbitrary processes. Our code is available at https://github.com/arpitbansal297/Cold-Diffusion-Models

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Diffusion models that are based on iterative denoising have been recently proposed and leveraged in various generation tasks like image generation. Whereas, as a way inherently built for continuous data, existing diffusion models still have some limitations in modeling discrete data, e.g., languages. For example, the generally used Gaussian noise can not handle the discrete corruption well, and the objectives in continuous spaces fail to be stable for textual data in the diffusion process especially when the dimension is high. To alleviate these issues, we introduce a novel diffusion model for language modeling, Masked-Diffuse LM, with lower training cost and better performances, inspired by linguistic features in languages. Specifically, we design a linguistic-informed forward process which adds corruptions to the text through strategically soft-masking to better noise the textual data. Also, we directly predict the categorical distribution with cross-entropy loss function in every diffusion step to connect the continuous space and discrete space in a more efficient and straightforward way. Through experiments on 5 controlled generation tasks, we demonstrate that our Masked-Diffuse LM can achieve better generation quality than the state-of-the-art diffusion models with better efficiency.

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear inverse problems in noiseless settings, which significantly under-represents the complexity of real-world problems. In this work, we extend diffusion solvers to efficiently handle general noisy (non)linear inverse problems via approximation of the posterior sampling. Interestingly, the resulting posterior sampling scheme is a blended version of diffusion sampling with the manifold constrained gradient without a strict measurement consistency projection step, yielding a more desirable generative path in noisy settings compared to the previous studies. Our method demonstrates that diffusion models can incorporate various measurement noise statistics such as Gaussian and Poisson, and also efficiently handle noisy nonlinear inverse problems such as Fourier phase retrieval and non-uniform deblurring. Code available at https://github.com/DPS2022/diffusion-posterior-sampling

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signal-leak bias is particularly significant when models are tuned to a specific style, causing sub-optimal style matching. Recent research tries to avoid the signal leakage during training. We instead show how we can exploit this signal-leak bias in existing diffusion models to allow more control over the generated images. This enables us to generate images with more varied brightness, and images that better match a desired style or color. By modeling the distribution of the signal leak in the spatial frequency and pixel domains, and including a signal leak in the initial latent, we generate images that better match expected results without any additional training.

Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.

Diffusion-based image restoration (IR) methods aim to use diffusion models to recover high-quality (HQ) images from degraded images and achieve promising performance. Due to the inherent property of diffusion models, most of these methods need long serial sampling chains to restore HQ images step-by-step. As a result, it leads to expensive sampling time and high computation costs. Moreover, such long sampling chains hinder understanding the relationship between the restoration results and the inputs since it is hard to compute the gradients in the whole chains. In this work, we aim to rethink the diffusion-based IR models through a different perspective, i.e., a deep equilibrium (DEQ) fixed point system. Specifically, we derive an analytical solution by modeling the entire sampling chain in diffusion-based IR models as a joint multivariate fixed point system. With the help of the analytical solution, we are able to conduct single-image sampling in a parallel way and restore HQ images without training. Furthermore, we compute fast gradients in DEQ and found that initialization optimization can boost performance and control the generation direction. Extensive experiments on benchmarks demonstrate the effectiveness of our proposed method on typical IR tasks and real-world settings. The code and models will be made publicly available.

Recent research explores the potential of Diffusion Models (DMs) for consistent object editing, which aims to modify object position, size, and composition, etc., while preserving the consistency of objects and background without changing their texture and attributes. Current inference-time methods often rely on DDIM inversion, which inherently compromises efficiency and the achievable consistency of edited images. Recent methods also utilize energy guidance which iteratively updates the predicted noise and can drive the latents away from the original image, resulting in distortions. In this paper, we propose PixelMan, an inversion-free and training-free method for achieving consistent object editing via Pixel Manipulation and generation, where we directly create a duplicate copy of the source object at target location in the pixel space, and introduce an efficient sampling approach to iteratively harmonize the manipulated object into the target location and inpaint its original location, while ensuring image consistency by anchoring the edited image to be generated to the pixel-manipulated image as well as by introducing various consistency-preserving optimization techniques during inference. Experimental evaluations based on benchmark datasets as well as extensive visual comparisons show that in as few as 16 inference steps, PixelMan outperforms a range of state-of-the-art training-based and training-free methods (usually requiring 50 steps) on multiple consistent object editing tasks.

This paper describes an efficient algorithm for solving noisy linear inverse problems using pretrained diffusion models. Extending the paradigm of denoising diffusion implicit models (DDIM), we propose constrained diffusion implicit models (CDIM) that modify the diffusion updates to enforce a constraint upon the final output. For noiseless inverse problems, CDIM exactly satisfies the constraints; in the noisy case, we generalize CDIM to satisfy an exact constraint on the residual distribution of the noise. Experiments across a variety of tasks and metrics show strong performance of CDIM, with analogous inference acceleration to unconstrained DDIM: 10 to 50 times faster than previous conditional diffusion methods. We demonstrate the versatility of our approach on many problems including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reconstruction.

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion models, have gained popularity in this area for their ability to produce realistic solutions and their good mathematical properties. Despite their success, an important drawback of diffusion models is their sensitivity to the choice of variance schedule, which controls the dynamics of the diffusion process. Fine-tuning this schedule for specific applications is crucial but time-costly and does not guarantee an optimal result. We propose a novel approach for learning the schedule as part of the training process. Our method supports probabilistic conditioning on data, provides high-quality solutions, and is flexible, proving able to adapt to different applications with minimum overhead. This approach is tested in two unrelated inverse problems: super-resolution microscopy and quantitative phase imaging, yielding comparable or superior results to previous methods and fine-tuned diffusion models. We conclude that fine-tuning the schedule by experimentation should be avoided because it can be learned during training in a stable way that yields better results.

Since their introduction, diffusion models have quickly become the prevailing approach to generative modeling in many domains. They can be interpreted as learning the gradients of a time-varying sequence of log-probability density functions. This interpretation has motivated classifier-based and classifier-free guidance as methods for post-hoc control of diffusion models. In this work, we build upon these ideas using the score-based interpretation of diffusion models, and explore alternative ways to condition, modify, and reuse diffusion models for tasks involving compositional generation and guidance. In particular, we investigate why certain types of composition fail using current techniques and present a number of solutions. We conclude that the sampler (not the model) is responsible for this failure and propose new samplers, inspired by MCMC, which enable successful compositional generation. Further, we propose an energy-based parameterization of diffusion models which enables the use of new compositional operators and more sophisticated, Metropolis-corrected samplers. Intriguingly we find these samplers lead to notable improvements in compositional generation across a wide set of problems such as classifier-guided ImageNet modeling and compositional text-to-image generation.

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive and unsuitable for real-time sequential inverse problems such as ultrasound imaging. Considering the strong temporal structure across sequences of frames, we propose a novel approach that models the transition dynamics to improve the efficiency of sequential diffusion posterior sampling in conditional image synthesis. Through modeling sequence data using a video vision transformer (ViViT) transition model based on previous diffusion outputs, we can initialize the reverse diffusion trajectory at a lower noise scale, greatly reducing the number of iterations required for convergence. We demonstrate the effectiveness of our approach on a real-world dataset of high frame rate cardiac ultrasound images and show that it achieves the same performance as a full diffusion trajectory while accelerating inference 25times, enabling real-time posterior sampling. Furthermore, we show that the addition of a transition model improves the PSNR up to 8\% in cases with severe motion. Our method opens up new possibilities for real-time applications of diffusion models in imaging and other domains requiring real-time inference.

Recent advances in Conditional Diffusion Models have led to substantial capabilities in various domains. However, understanding the impact of variations in the initial seed vector remains an underexplored area of concern. Particularly, latent-based diffusion models display inconsistencies in image generation under standard conditions when initialized with suboptimal initial seed vectors. To understand the impact of the initial seed vector on generated samples, we propose a reliability evaluation framework that evaluates the generated samples of a diffusion model when the initial seed vector is subjected to various synthetic shifts. Our results indicate that slight manipulations to the initial seed vector of the state-of-the-art Stable Diffusion (Rombach et al., 2022) can lead to significant disturbances in the generated samples, consequently creating images without the effect of conditioning variables. In contrast, GLIDE (Nichol et al., 2022) stands out in generating reliable samples even when the initial seed vector is transformed. Thus, our study sheds light on the importance of the selection and the impact of the initial seed vector in the latent-based diffusion model.

We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important, since they often contain some unique attributes of the data. However, the conventional generation process of the diffusion models mostly yields majority samples (that lie on high-density regions of the manifold) due to their high likelihoods, making themselves ineffective and time-consuming for the minority generating task. In this work, we present a novel framework that can make the generation process of the diffusion models focus on the minority samples. We first highlight that Tweedie's denoising formula yields favorable results for majority samples. The observation motivates us to introduce a metric that describes the uniqueness of a given sample. To address the inherent preference of the diffusion models w.r.t. the majority samples, we further develop minority guidance, a sampling technique that can guide the generation process toward regions with desired likelihood levels. Experiments on benchmark real datasets demonstrate that our minority guidance can greatly improve the capability of generating high-quality minority samples over existing generative samplers. We showcase that the performance benefit of our framework persists even in demanding real-world scenarios such as medical imaging, further underscoring the practical significance of our work. Code is available at https://github.com/soobin-um/minority-guidance.

We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.

Diffusion inversion is the problem of taking an image and a text prompt that describes it and finding a noise latent that would generate the image. Most current inversion techniques operate by approximately solving an implicit equation and may converge slowly or yield poor reconstructed images. Here, we formulate the problem as finding the roots of an implicit equation and design a method to solve it efficiently. Our solution is based on Newton-Raphson (NR), a well-known technique in numerical analysis. A naive application of NR may be computationally infeasible and tends to converge to incorrect solutions. We describe an efficient regularized formulation that converges quickly to a solution that provides high-quality reconstructions. We also identify a source of inconsistency stemming from prompt conditioning during the inversion process, which significantly degrades the inversion quality. To address this, we introduce a prompt-aware adjustment of the encoding, effectively correcting this issue. Our solution, Regularized Newton-Raphson Inversion, inverts an image within 0.5 sec for latent consistency models, opening the door for interactive image editing. We further demonstrate improved results in image interpolation and generation of rare objects.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

Diffusion-based Image Editing (DIE) is an emerging research hot-spot, which often applies a semantic mask to control the target area for diffusion-based editing. However, most existing solutions obtain these masks via manual operations or off-line processing, greatly reducing their efficiency. In this paper, we propose a novel and efficient image editing method for Text-to-Image (T2I) diffusion models, termed Instant Diffusion Editing(InstDiffEdit). In particular, InstDiffEdit aims to employ the cross-modal attention ability of existing diffusion models to achieve instant mask guidance during the diffusion steps. To reduce the noise of attention maps and realize the full automatics, we equip InstDiffEdit with a training-free refinement scheme to adaptively aggregate the attention distributions for the automatic yet accurate mask generation. Meanwhile, to supplement the existing evaluations of DIE, we propose a new benchmark called Editing-Mask to examine the mask accuracy and local editing ability of existing methods. To validate InstDiffEdit, we also conduct extensive experiments on ImageNet and Imagen, and compare it with a bunch of the SOTA methods. The experimental results show that InstDiffEdit not only outperforms the SOTA methods in both image quality and editing results, but also has a much faster inference speed, i.e., +5 to +6 times.

Diffusion models have demonstrated remarkable generation quality but at the cost of numerous function evaluations. Recently, advanced ODE-based solvers have been developed to mitigate the substantial computational demands of reverse-diffusion solving under limited sampling steps. However, these solvers, heavily inspired by Adams-like multistep methods, rely solely on t-related Lagrange interpolation. We show that t-related Lagrange interpolation is suboptimal for diffusion model and reveal a compact search space comprised of time steps and solver coefficients. Building on our analysis, we propose a novel differentiable solver search algorithm to identify more optimal solver. Equipped with the searched solver, rectified-flow models, e.g., SiT-XL/2 and FlowDCN-XL/2, achieve FID scores of 2.40 and 2.35, respectively, on ImageNet256 with only 10 steps. Meanwhile, DDPM model, DiT-XL/2, reaches a FID score of 2.33 with only 10 steps. Notably, our searched solver outperforms traditional solvers by a significant margin. Moreover, our searched solver demonstrates generality across various model architectures, resolutions, and model sizes.

As one of the most successful generative models, diffusion models have demonstrated remarkable efficacy in synthesizing high-quality images. These models learn the underlying high-dimensional data distribution in an unsupervised manner. Despite their success, diffusion models are highly data-driven and prone to inheriting the imbalances and biases present in real-world data. Some studies have attempted to address these issues by designing text prompts for known biases or using bias labels to construct unbiased data. While these methods have shown improved results, real-world scenarios often contain various unknown biases, and obtaining bias labels is particularly challenging. In this paper, we emphasize the necessity of mitigating bias in pre-trained diffusion models without relying on auxiliary bias annotations. To tackle this problem, we propose a framework, InvDiff, which aims to learn invariant semantic information for diffusion guidance. Specifically, we propose identifying underlying biases in the training data and designing a novel debiasing training objective. Then, we employ a lightweight trainable module that automatically preserves invariant semantic information and uses it to guide the diffusion model's sampling process toward unbiased outcomes simultaneously. Notably, we only need to learn a small number of parameters in the lightweight learnable module without altering the pre-trained diffusion model. Furthermore, we provide a theoretical guarantee that the implementation of InvDiff is equivalent to reducing the error upper bound of generalization. Extensive experimental results on three publicly available benchmarks demonstrate that InvDiff effectively reduces biases while maintaining the quality of image generation. Our code is available at https://github.com/Hundredl/InvDiff.

Diffusion models are the current state of the art for generating photorealistic images. Controlling the sampling process for constrained image generation tasks such as inpainting, however, remains challenging since exact conditioning on such constraints is intractable. While existing methods use various techniques to approximate the constrained posterior, this paper proposes to exploit the ability of Tractable Probabilistic Models (TPMs) to exactly and efficiently compute the constrained posterior, and to leverage this signal to steer the denoising process of diffusion models. Specifically, this paper adopts a class of expressive TPMs termed Probabilistic Circuits (PCs). Building upon prior advances, we further scale up PCs and make them capable of guiding the image generation process of diffusion models. Empirical results suggest that our approach can consistently improve the overall quality and semantic coherence of inpainted images across three natural image datasets (i.e., CelebA-HQ, ImageNet, and LSUN) with only ~10% additional computational overhead brought by the TPM. Further, with the help of an image encoder and decoder, our method can readily accept semantic constraints on specific regions of the image, which opens up the potential for more controlled image generation tasks. In addition to proposing a new framework for constrained image generation, this paper highlights the benefit of more tractable models and motivates the development of expressive TPMs.

Following the remarkable success of diffusion models on image generation, recent works have also demonstrated their impressive ability to address a number of inverse problems in an unsupervised way, by properly constraining the sampling process based on a conditioning input. Motivated by this, in this paper, we present the first approach to use diffusion models as a prior for highly accurate 3D facial BRDF reconstruction from a single image. We start by leveraging a high-quality UV dataset of facial reflectance (diffuse and specular albedo and normals), which we render under varying illumination settings to simulate natural RGB textures and, then, train an unconditional diffusion model on concatenated pairs of rendered textures and reflectance components. At test time, we fit a 3D morphable model to the given image and unwrap the face in a partial UV texture. By sampling from the diffusion model, while retaining the observed texture part intact, the model inpaints not only the self-occluded areas but also the unknown reflectance components, in a single sequence of denoising steps. In contrast to existing methods, we directly acquire the observed texture from the input image, thus, resulting in more faithful and consistent reflectance estimation. Through a series of qualitative and quantitative comparisons, we demonstrate superior performance in both texture completion as well as reflectance reconstruction tasks.

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in 5sim 10 function evaluations.

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 4.12 for CIFAR-10 and 8.35 for ImageNet-64 in the one-model-evaluation setting.

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a 4sim 16times speedup compared with previous state-of-the-art training-free samplers on various datasets.

We introduce a novel approach for concept blending in pretrained text-to-image diffusion models, aiming to generate images at the intersection of multiple text prompts. At each time step during diffusion denoising, our algorithm forecasts predictions w.r.t. the generated image and makes informed text conditioning decisions. Central to our method is the unique analogy between diffusion models, which are rooted in non-equilibrium thermodynamics, and the Black-Scholes model for financial option pricing. By drawing parallels between key variables in both domains, we derive a robust algorithm for concept blending that capitalizes on the Markovian dynamics of the Black-Scholes framework. Our text-based concept blending algorithm is data-efficient, meaning it does not need additional training. Furthermore, it operates without human intervention or hyperparameter tuning. We highlight the benefits of our approach by comparing it qualitatively and quantitatively to other text based concept blending techniques, including linear interpolation, alternating prompts, step-wise prompt switching, and CLIP-guided prompt selection across various scenarios such as single object per text prompt, multiple objects per text prompt and objects against backgrounds. Our work shows that financially inspired techniques can enhance text-to-image concept blending in generative AI, paving the way for broader innovation. Code is available at https://github.com/divyakraman/BlackScholesDiffusion2024.

We present a cascaded diffusion model based on a part-level implicit 3D representation. Our model achieves state-of-the-art generation quality and also enables part-level shape editing and manipulation without any additional training in conditional setup. Diffusion models have demonstrated impressive capabilities in data generation as well as zero-shot completion and editing via a guided reverse process. Recent research on 3D diffusion models has focused on improving their generation capabilities with various data representations, while the absence of structural information has limited their capability in completion and editing tasks. We thus propose our novel diffusion model using a part-level implicit representation. To effectively learn diffusion with high-dimensional embedding vectors of parts, we propose a cascaded framework, learning diffusion first on a low-dimensional subspace encoding extrinsic parameters of parts and then on the other high-dimensional subspace encoding intrinsic attributes. In the experiments, we demonstrate the outperformance of our method compared with the previous ones both in generation and part-level completion and manipulation tasks.

Image denoising is a fundamental problem in computational photography, where achieving high perception with low distortion is highly demanding. Current methods either struggle with perceptual quality or suffer from significant distortion. Recently, the emerging diffusion model has achieved state-of-the-art performance in various tasks and demonstrates great potential for image denoising. However, stimulating diffusion models for image denoising is not straightforward and requires solving several critical problems. For one thing, the input inconsistency hinders the connection between diffusion models and image denoising. For another, the content inconsistency between the generated image and the desired denoised image introduces distortion. To tackle these problems, we present a novel strategy called the Diffusion Model for Image Denoising (DMID) by understanding and rethinking the diffusion model from a denoising perspective. Our DMID strategy includes an adaptive embedding method that embeds the noisy image into a pre-trained unconditional diffusion model and an adaptive ensembling method that reduces distortion in the denoised image. Our DMID strategy achieves state-of-the-art performance on both distortion-based and perception-based metrics, for both Gaussian and real-world image denoising.The code is available at https://github.com/Li-Tong-621/DMID.

When solving inverse problems, it is increasingly popular to use pre-trained diffusion models as plug-and-play priors. This framework can accommodate different forward models without re-training while preserving the generative capability of diffusion models. Despite their success in many imaging inverse problems, most existing methods rely on privileged information such as derivative, pseudo-inverse, or full knowledge about the forward model. This reliance poses a substantial limitation that restricts their use in a wide range of problems where such information is unavailable, such as in many scientific applications. To address this issue, we propose Ensemble Kalman Diffusion Guidance (EnKG) for diffusion models, a derivative-free approach that can solve inverse problems by only accessing forward model evaluations and a pre-trained diffusion model prior. We study the empirical effectiveness of our method across various inverse problems, including scientific settings such as inferring fluid flows and astronomical objects, which are highly non-linear inverse problems that often only permit black-box access to the forward model.

Recently, there has been tremendous progress in visual synthesis and the underlying generative models. Here, diffusion models (DMs) stand out particularly, but lately, flow matching (FM) has also garnered considerable interest. While DMs excel in providing diverse images, they suffer from long training and slow generation. With latent diffusion, these issues are only partially alleviated. Conversely, FM offers faster training and inference but exhibits less diversity in synthesis. We demonstrate that introducing FM between the Diffusion model and the convolutional decoder offers high-resolution image synthesis with reduced computational cost and model size. Diffusion can then efficiently provide the necessary generation diversity. FM compensates for the lower resolution, mapping the small latent space to a high-dimensional one. Subsequently, the convolutional decoder of the LDM maps these latents to high-resolution images. By combining the diversity of DMs, the efficiency of FMs, and the effectiveness of convolutional decoders, we achieve state-of-the-art high-resolution image synthesis at 1024^2 with minimal computational cost. Importantly, our approach is orthogonal to recent approximation and speed-up strategies for the underlying DMs, making it easily integrable into various DM frameworks.

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we present a novel method based on the expectation-maximization algorithm for training diffusion models from incomplete and noisy observations only. Unlike previous works, our method leads to proper diffusion models, which is crucial for downstream tasks. As part of our method, we propose and motivate an improved posterior sampling scheme for unconditional diffusion models. We present empirical evidence supporting the effectiveness of our method.

Recent advances in text-to-image generation with diffusion models present transformative capabilities in image quality. However, user controllability of the generated image, and fast adaptation to new tasks still remains an open challenge, currently mostly addressed by costly and long re-training and fine-tuning or ad-hoc adaptations to specific image generation tasks. In this work, we present MultiDiffusion, a unified framework that enables versatile and controllable image generation, using a pre-trained text-to-image diffusion model, without any further training or finetuning. At the center of our approach is a new generation process, based on an optimization task that binds together multiple diffusion generation processes with a shared set of parameters or constraints. We show that MultiDiffusion can be readily applied to generate high quality and diverse images that adhere to user-provided controls, such as desired aspect ratio (e.g., panorama), and spatial guiding signals, ranging from tight segmentation masks to bounding boxes. Project webpage: https://multidiffusion.github.io

Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples that are highly diverse and representative of the underlying distribution. However, one of the main limitations of diffusion models is the complexity of sample generation, since a large number of inference timesteps is required to faithfully capture the data distribution. In this paper, we present MMD-DDM, a novel method for fast sampling of diffusion models. Our approach is based on the idea of using the Maximum Mean Discrepancy (MMD) to finetune the learned distribution with a given budget of timesteps. This allows the finetuned model to significantly improve the speed-quality trade-off, by substantially increasing fidelity in inference regimes with few steps or, equivalently, by reducing the required number of steps to reach a target fidelity, thus paving the way for a more practical adoption of diffusion models in a wide range of applications. We evaluate our approach on unconditional image generation with extensive experiments across the CIFAR-10, CelebA, ImageNet and LSUN-Church datasets. Our findings show that the proposed method is able to produce high-quality samples in a fraction of the time required by widely-used diffusion models, and outperforms state-of-the-art techniques for accelerated sampling. Code is available at: https://github.com/diegovalsesia/MMD-DDM.

We derive a minimalist but powerful deterministic denoising-diffusion model. While denoising diffusion has shown great success in many domains, its underlying theory remains largely inaccessible to non-expert users. Indeed, an understanding of graduate-level concepts such as Langevin dynamics or score matching appears to be required to grasp how it works. We propose an alternative approach that requires no more than undergrad calculus and probability. We consider two densities and observe what happens when random samples from these densities are blended (linearly interpolated). We show that iteratively blending and deblending samples produces random paths between the two densities that converge toward a deterministic mapping. This mapping can be evaluated with a neural network trained to deblend samples. We obtain a model that behaves like deterministic denoising diffusion: it iteratively maps samples from one density (e.g., Gaussian noise) to another (e.g., cat images). However, compared to the state-of-the-art alternative, our model is simpler to derive, simpler to implement, more numerically stable, achieves higher quality results in our experiments, and has interesting connections to computer graphics.

Echocardiography has been a prominent tool for the diagnosis of cardiac disease. However, these diagnoses can be heavily impeded by poor image quality. Acoustic clutter emerges due to multipath reflections imposed by layers of skin, subcutaneous fat, and intercostal muscle between the transducer and heart. As a result, haze and other noise artifacts pose a real challenge to cardiac ultrasound imaging. In many cases, especially with difficult-to-image patients such as patients with obesity, a diagnosis from B-Mode ultrasound imaging is effectively rendered unusable, forcing sonographers to resort to contrast-enhanced ultrasound examinations or refer patients to other imaging modalities. Tissue harmonic imaging has been a popular approach to combat haze, but in severe cases is still heavily impacted by haze. Alternatively, denoising algorithms are typically unable to remove highly structured and correlated noise, such as haze. It remains a challenge to accurately describe the statistical properties of structured haze, and develop an inference method to subsequently remove it. Diffusion models have emerged as powerful generative models and have shown their effectiveness in a variety of inverse problems. In this work, we present a joint posterior sampling framework that combines two separate diffusion models to model the distribution of both clean ultrasound and haze in an unsupervised manner. Furthermore, we demonstrate techniques for effectively training diffusion models on radio-frequency ultrasound data and highlight the advantages over image data. Experiments on both in-vitro and in-vivo cardiac datasets show that the proposed dehazing method effectively removes haze while preserving signals from weakly reflected tissue.

Probabilistic diffusion models have achieved state-of-the-art results for image synthesis, inpainting, and text-to-image tasks. However, they are still in the early stages of generating complex 3D shapes. This work proposes Diffusion-SDF, a generative model for shape completion, single-view reconstruction, and reconstruction of real-scanned point clouds. We use neural signed distance functions (SDFs) as our 3D representation to parameterize the geometry of various signals (e.g., point clouds, 2D images) through neural networks. Neural SDFs are implicit functions and diffusing them amounts to learning the reversal of their neural network weights, which we solve using a custom modulation module. Extensive experiments show that our method is capable of both realistic unconditional generation and conditional generation from partial inputs. This work expands the domain of diffusion models from learning 2D, explicit representations, to 3D, implicit representations.

Recently, diffusion models have exhibited superior performance in the area of image inpainting. Inpainting methods based on diffusion models can usually generate realistic, high-quality image content for masked areas. However, due to the limitations of diffusion models, existing methods typically encounter problems in terms of semantic consistency between images and text, and the editing habits of users. To address these issues, we present PainterNet, a plugin that can be flexibly embedded into various diffusion models. To generate image content in the masked areas that highly aligns with the user input prompt, we proposed local prompt input, Attention Control Points (ACP), and Actual-Token Attention Loss (ATAL) to enhance the model's focus on local areas. Additionally, we redesigned the MASK generation algorithm in training and testing dataset to simulate the user's habit of applying MASK, and introduced a customized new training dataset, PainterData, and a benchmark dataset, PainterBench. Our extensive experimental analysis exhibits that PainterNet surpasses existing state-of-the-art models in key metrics including image quality and global/local text consistency.

Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.

We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at different times, and on different distributions and domains and can be later composed to achieve performance comparable to a paragon model trained on all data simultaneously. Furthermore, each model only contains information about the subset of the data it was exposed to during training, enabling several forms of training data protection. In particular, CDMs are the first method to enable both selective forgetting and continual learning for large-scale diffusion models, as well as allowing serving customized models based on the user's access rights. CDMs also allow determining the importance of a subset of the data in generating particular samples.

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by building a diffusion process, directly bridging the clean and the corrupted for specific inverse problems. In this paper, we first unify these existing works under the name Direct Diffusion Bridges (DDB), showing that while motivated by different theories, the resulting algorithms only differ in the choice of parameters. Then, we highlight a critical limitation of the current DDB framework, namely that it does not ensure data consistency. To address this problem, we propose a modified inference procedure that imposes data consistency without the need for fine-tuning. We term the resulting method data Consistent DDB (CDDB), which outperforms its inconsistent counterpart in terms of both perception and distortion metrics, thereby effectively pushing the Pareto-frontier toward the optimum. Our proposed method achieves state-of-the-art results on both evaluation criteria, showcasing its superiority over existing methods.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Diffusion models have achieved remarkable success in image generation tasks, yet their practical deployment is restrained by the high memory and time consumption. While quantization paves a way for diffusion model compression and acceleration, existing methods totally fail when the models are quantized to low-bits. In this paper, we unravel three properties in quantized diffusion models that compromise the efficacy of current methods: imbalanced activation distributions, imprecise temporal information, and vulnerability to perturbations of specific modules. To alleviate the intensified low-bit quantization difficulty stemming from the distribution imbalance, we propose finetuning the quantized model to better adapt to the activation distribution. Building on this idea, we identify two critical types of quantized layers: those holding vital temporal information and those sensitive to reduced bit-width, and finetune them to mitigate performance degradation with efficiency. We empirically verify that our approach modifies the activation distribution and provides meaningful temporal information, facilitating easier and more accurate quantization. Our method is evaluated over three high-resolution image generation tasks and achieves state-of-the-art performance under various bit-width settings, as well as being the first method to generate readable images on full 4-bit (i.e. W4A4) Stable Diffusion. Code is been made publicly available.

Latent diffusion models have become the popular choice for scaling up diffusion models for high resolution image synthesis. Compared to pixel-space models that are trained end-to-end, latent models are perceived to be more efficient and to produce higher image quality at high resolution. Here we challenge these notions, and show that pixel-space models can in fact be very competitive to latent approaches both in quality and efficiency, achieving 1.5 FID on ImageNet512 and new SOTA results on ImageNet128 and ImageNet256. We present a simple recipe for scaling end-to-end pixel-space diffusion models to high resolutions. 1: Use the sigmoid loss (Kingma & Gao, 2023) with our prescribed hyper-parameters. 2: Use our simplified memory-efficient architecture with fewer skip-connections. 3: Scale the model to favor processing the image at high resolution with fewer parameters, rather than using more parameters but at a lower resolution. When combining these three steps with recently proposed tricks like guidance intervals, we obtain a family of pixel-space diffusion models we call Simple Diffusion v2 (SiD2).

Recent advancements in text-guided diffusion models have unlocked powerful image manipulation capabilities, yet balancing reconstruction fidelity and editability for real images remains a significant challenge. In this work, we introduce Task-Oriented Diffusion Inversion (TODInv), a novel framework that inverts and edits real images tailored to specific editing tasks by optimizing prompt embeddings within the extended \(P^*\) space. By leveraging distinct embeddings across different U-Net layers and time steps, TODInv seamlessly integrates inversion and editing through reciprocal optimization, ensuring both high fidelity and precise editability. This hierarchical editing mechanism categorizes tasks into structure, appearance, and global edits, optimizing only those embeddings unaffected by the current editing task. Extensive experiments on benchmark dataset reveal TODInv's superior performance over existing methods, delivering both quantitative and qualitative enhancements while showcasing its versatility with few-step diffusion model.

Denoising diffusion models have emerged as the go-to framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution (OOD) tasks, which remains an under-explored challenge. Realistic reconstructions inconsistent with the measured data can be generated, hallucinating image features that are uniquely present in the training dataset. To simultaneously enforce data-consistency and leverage data-driven priors, we introduce a novel sampling framework called Steerable Conditional Diffusion. This framework adapts the denoising network specifically to the available measured data. Utilising our proposed method, we achieve substantial enhancements in OOD performance across diverse imaging modalities, advancing the robust deployment of denoising diffusion models in real-world applications.

Diffusion models have achieved unprecedented performance in generative modeling. The commonly-adopted formulation of the latent code of diffusion models is a sequence of gradually denoised samples, as opposed to the simpler (e.g., Gaussian) latent space of GANs, VAEs, and normalizing flows. This paper provides an alternative, Gaussian formulation of the latent space of various diffusion models, as well as an invertible DPM-Encoder that maps images into the latent space. While our formulation is purely based on the definition of diffusion models, we demonstrate several intriguing consequences. (1) Empirically, we observe that a common latent space emerges from two diffusion models trained independently on related domains. In light of this finding, we propose CycleDiffusion, which uses DPM-Encoder for unpaired image-to-image translation. Furthermore, applying CycleDiffusion to text-to-image diffusion models, we show that large-scale text-to-image diffusion models can be used as zero-shot image-to-image editors. (2) One can guide pre-trained diffusion models and GANs by controlling the latent codes in a unified, plug-and-play formulation based on energy-based models. Using the CLIP model and a face recognition model as guidance, we demonstrate that diffusion models have better coverage of low-density sub-populations and individuals than GANs. The code is publicly available at https://github.com/ChenWu98/cycle-diffusion.

Score-based diffusion models have emerged as one of the most promising frameworks for deep generative modelling, due to their state-of-the art performance in many generation tasks while relying on mathematical foundations such as stochastic differential equations (SDEs) and ordinary differential equations (ODEs). Empirically, it has been reported that ODE based samples are inferior to SDE based samples. In this paper we rigorously describe the range of dynamics and approximations that arise when training score-based diffusion models, including the true SDE dynamics, the neural approximations, the various approximate particle dynamics that result, as well as their associated Fokker--Planck equations and the neural network approximations of these Fokker--Planck equations. We systematically analyse the difference between the ODE and SDE dynamics of score-based diffusion models, and link it to an associated Fokker--Planck equation. We derive a theoretical upper bound on the Wasserstein 2-distance between the ODE- and SDE-induced distributions in terms of a Fokker--Planck residual. We also show numerically that conventional score-based diffusion models can exhibit significant differences between ODE- and SDE-induced distributions which we demonstrate using explicit comparisons. Moreover, we show numerically that reducing the Fokker--Planck residual by adding it as an additional regularisation term leads to closing the gap between ODE- and SDE-induced distributions. Our experiments suggest that this regularisation can improve the distribution generated by the ODE, however that this can come at the cost of degraded SDE sample quality.

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs

In medical imaging, the diffusion models have shown great potential in synthetic image generation tasks. However, these models often struggle with the interpretable connections between the generated and existing images and could create illusions. To address these challenges, our research proposes a novel diffusion-based generative model based on deformation diffusion and recovery. This model, named Deformation-Recovery Diffusion Model (DRDM), diverges from traditional score/intensity and latent feature-based approaches, emphasizing morphological changes through deformation fields rather than direct image synthesis. This is achieved by introducing a topological-preserving deformation field generation method, which randomly samples and integrates a set of multi-scale Deformation Vector Fields (DVF). DRDM is trained to learn to recover unreasonable deformation components, thereby restoring each randomly deformed image to a realistic distribution. These innovations facilitate the generation of diverse and anatomically plausible deformations, enhancing data augmentation and synthesis for further analysis in downstream tasks, such as few-shot learning and image registration. Experimental results in cardiac MRI and pulmonary CT show DRDM is capable of creating diverse, large (over 10\% image size deformation scale), and high-quality (negative rate of the Jacobian matrix's determinant is lower than 1\%) deformation fields. The further experimental results in downstream tasks, 2D image segmentation and 3D image registration, indicate significant improvements resulting from DRDM, showcasing the potential of our model to advance image manipulation and synthesis in medical imaging and beyond. Project page: https://jianqingzheng.github.io/def_diff_rec/

Diffusion models exhibited tremendous progress in image and video generation, exceeding GANs in quality and diversity. However, they are usually trained on very large datasets and are not naturally adapted to manipulate a given input image or video. In this paper we show how this can be resolved by training a diffusion model on a single input image or video. Our image/video-specific diffusion model (SinFusion) learns the appearance and dynamics of the single image or video, while utilizing the conditioning capabilities of diffusion models. It can solve a wide array of image/video-specific manipulation tasks. In particular, our model can learn from few frames the motion and dynamics of a single input video. It can then generate diverse new video samples of the same dynamic scene, extrapolate short videos into long ones (both forward and backward in time) and perform video upsampling. Most of these tasks are not realizable by current video-specific generation methods.

The correct insertion of virtual objects in images of real-world scenes requires a deep understanding of the scene's lighting, geometry and materials, as well as the image formation process. While recent large-scale diffusion models have shown strong generative and inpainting capabilities, we find that current models do not sufficiently "understand" the scene shown in a single picture to generate consistent lighting effects (shadows, bright reflections, etc.) while preserving the identity and details of the composited object. We propose using a personalized large diffusion model as guidance to a physically based inverse rendering process. Our method recovers scene lighting and tone-mapping parameters, allowing the photorealistic composition of arbitrary virtual objects in single frames or videos of indoor or outdoor scenes. Our physically based pipeline further enables automatic materials and tone-mapping refinement.

Diffusion model-based inverse problem solvers have demonstrated state-of-the-art performance in cases where the forward operator is known (i.e. non-blind). However, the applicability of the method to blind inverse problems has yet to be explored. In this work, we show that we can indeed solve a family of blind inverse problems by constructing another diffusion prior for the forward operator. Specifically, parallel reverse diffusion guided by gradients from the intermediate stages enables joint optimization of both the forward operator parameters as well as the image, such that both are jointly estimated at the end of the parallel reverse diffusion procedure. We show the efficacy of our method on two representative tasks -- blind deblurring, and imaging through turbulence -- and show that our method yields state-of-the-art performance, while also being flexible to be applicable to general blind inverse problems when we know the functional forms.

Diffusion models have demonstrated impressive abilities in generating photo-realistic and creative images. To offer more controllability for the generation process, existing studies, termed as early-constraint methods in this paper, leverage extra conditions and incorporate them into pre-trained diffusion models. Particularly, some of them adopt condition-specific modules to handle conditions separately, where they struggle to generalize across other conditions. Although follow-up studies present unified solutions to solve the generalization problem, they also require extra resources to implement, e.g., additional inputs or parameter optimization, where more flexible and efficient solutions are expected to perform steerable guided image synthesis. In this paper, we present an alternative paradigm, namely Late-Constraint Diffusion (LaCon), to simultaneously integrate various conditions into pre-trained diffusion models. Specifically, LaCon establishes an alignment between the external condition and the internal features of diffusion models, and utilizes the alignment to incorporate the target condition, guiding the sampling process to produce tailored results. Experimental results on COCO dataset illustrate the effectiveness and superior generalization capability of LaCon under various conditions and settings. Ablation studies investigate the functionalities of different components in LaCon, and illustrate its great potential to serve as an efficient solution to offer flexible controllability for diffusion models.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their generalizability to various degradation scenarios. To address this limitation, we propose a zero-shot framework capable of handling various imaging inverse problems without model retraining. We introduce a likelihood-guided noise refinement mechanism that derives a closed-form approximation of the likelihood score, simplifying score estimation and avoiding expensive gradient computations. This estimated score is subsequently utilized to refine the model-predicted noise, thereby better aligning the restoration process with the generative framework of diffusion models. In addition, we integrate the Denoising Diffusion Implicit Models (DDIM) sampling strategy to further improve inference efficiency. The proposed mechanism can be applied to both optimization-based and sampling-based schemes, providing an effective and flexible zero-shot solution for imaging inverse problems. Extensive experiments demonstrate that our method achieves superior performance across multiple inverse problems, particularly in compressive sensing, delivering high-quality reconstructions even at an extremely low sampling rate (5%).

Diffusion models have shown incredible capabilities as generative models; indeed, they power the current state-of-the-art models on text-conditioned image generation such as Imagen and DALL-E 2. In this work we review, demystify, and unify the understanding of diffusion models across both variational and score-based perspectives. We first derive Variational Diffusion Models (VDM) as a special case of a Markovian Hierarchical Variational Autoencoder, where three key assumptions enable tractable computation and scalable optimization of the ELBO. We then prove that optimizing a VDM boils down to learning a neural network to predict one of three potential objectives: the original source input from any arbitrary noisification of it, the original source noise from any arbitrarily noisified input, or the score function of a noisified input at any arbitrary noise level. We then dive deeper into what it means to learn the score function, and connect the variational perspective of a diffusion model explicitly with the Score-based Generative Modeling perspective through Tweedie's Formula. Lastly, we cover how to learn a conditional distribution using diffusion models via guidance.

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation.

Recent text-to-image diffusion models have demonstrated an astonishing capacity to generate high-quality images. However, researchers mainly studied the way of synthesizing images with only text prompts. While some works have explored using other modalities as conditions, considerable paired data, e.g., box/mask-image pairs, and fine-tuning time are required for nurturing models. As such paired data is time-consuming and labor-intensive to acquire and restricted to a closed set, this potentially becomes the bottleneck for applications in an open world. This paper focuses on the simplest form of user-provided conditions, e.g., box or scribble. To mitigate the aforementioned problem, we propose a training-free method to control objects and contexts in the synthesized images adhering to the given spatial conditions. Specifically, three spatial constraints, i.e., Inner-Box, Outer-Box, and Corner Constraints, are designed and seamlessly integrated into the denoising step of diffusion models, requiring no additional training and massive annotated layout data. Extensive results show that the proposed constraints can control what and where to present in the images while retaining the ability of the Stable Diffusion model to synthesize with high fidelity and diverse concept coverage. The code is publicly available at https://github.com/Sierkinhane/BoxDiff.

Plug-and-play Image Restoration (IR) has been widely recognized as a flexible and interpretable method for solving various inverse problems by utilizing any off-the-shelf denoiser as the implicit image prior. However, most existing methods focus on discriminative Gaussian denoisers. Although diffusion models have shown impressive performance for high-quality image synthesis, their potential to serve as a generative denoiser prior to the plug-and-play IR methods remains to be further explored. While several other attempts have been made to adopt diffusion models for image restoration, they either fail to achieve satisfactory results or typically require an unacceptable number of Neural Function Evaluations (NFEs) during inference. This paper proposes DiffPIR, which integrates the traditional plug-and-play method into the diffusion sampling framework. Compared to plug-and-play IR methods that rely on discriminative Gaussian denoisers, DiffPIR is expected to inherit the generative ability of diffusion models. Experimental results on three representative IR tasks, including super-resolution, image deblurring, and inpainting, demonstrate that DiffPIR achieves state-of-the-art performance on both the FFHQ and ImageNet datasets in terms of reconstruction faithfulness and perceptual quality with no more than 100 NFEs. The source code is available at {https://github.com/yuanzhi-zhu/DiffPIR}

Diffusion models are emerging models that generate images by iteratively denoising random Gaussian noise using deep neural networks. These models typically exhibit high computational and memory demands, necessitating effective post-training quantization for high-performance inference. Recent works propose low-bitwidth (e.g., 8-bit or 4-bit) quantization for diffusion models, however 4-bit integer quantization typically results in low-quality images. We observe that on several widely used hardware platforms, there is little or no difference in compute capability between floating-point and integer arithmetic operations of the same bitwidth (e.g., 8-bit or 4-bit). Therefore, we propose an effective floating-point quantization method for diffusion models that provides better image quality compared to integer quantization methods. We employ a floating-point quantization method that was effective for other processing tasks, specifically computer vision and natural language tasks, and tailor it for diffusion models by integrating weight rounding learning during the mapping of the full-precision values to the quantized values in the quantization process. We comprehensively study integer and floating-point quantization methods in state-of-the-art diffusion models. Our floating-point quantization method not only generates higher-quality images than that of integer quantization methods, but also shows no noticeable degradation compared to full-precision models (32-bit floating-point), when both weights and activations are quantized to 8-bit floating-point values, while has minimal degradation with 4-bit weights and 8-bit activations.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

Diffusion probabilistic models (DPMs) have exhibited excellent performance for high-fidelity image generation while suffering from inefficient sampling. Recent works accelerate the sampling procedure by proposing fast ODE solvers that leverage the specific ODE form of DPMs. However, they highly rely on specific parameterization during inference (such as noise/data prediction), which might not be the optimal choice. In this work, we propose a novel formulation towards the optimal parameterization during sampling that minimizes the first-order discretization error of the ODE solution. Based on such formulation, we propose DPM-Solver-v3, a new fast ODE solver for DPMs by introducing several coefficients efficiently computed on the pretrained model, which we call empirical model statistics. We further incorporate multistep methods and a predictor-corrector framework, and propose some techniques for improving sample quality at small numbers of function evaluations (NFE) or large guidance scales. Experiments show that DPM-Solver-v3 achieves consistently better or comparable performance in both unconditional and conditional sampling with both pixel-space and latent-space DPMs, especially in 5sim10 NFEs. We achieve FIDs of 12.21 (5 NFE), 2.51 (10 NFE) on unconditional CIFAR10, and MSE of 0.55 (5 NFE, 7.5 guidance scale) on Stable Diffusion, bringing a speed-up of 15\%sim30\% compared to previous state-of-the-art training-free methods. Code is available at https://github.com/thu-ml/DPM-Solver-v3.

Diffusion models have emerged as a popular method for 3D generation. However, it is still challenging for diffusion models to efficiently generate diverse and high-quality 3D shapes. In this paper, we introduce OctFusion, which can generate 3D shapes with arbitrary resolutions in 2.5 seconds on a single Nvidia 4090 GPU, and the extracted meshes are guaranteed to be continuous and manifold. The key components of OctFusion are the octree-based latent representation and the accompanying diffusion models. The representation combines the benefits of both implicit neural representations and explicit spatial octrees and is learned with an octree-based variational autoencoder. The proposed diffusion model is a unified multi-scale U-Net that enables weights and computation sharing across different octree levels and avoids the complexity of widely used cascaded diffusion schemes. We verify the effectiveness of OctFusion on the ShapeNet and Objaverse datasets and achieve state-of-the-art performances on shape generation tasks. We demonstrate that OctFusion is extendable and flexible by generating high-quality color fields for textured mesh generation and high-quality 3D shapes conditioned on text prompts, sketches, or category labels. Our code and pre-trained models are available at https://github.com/octree-nn/octfusion.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

In recent advancements in high-fidelity image generation, Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a key player. However, their application at high resolutions presents significant computational challenges. Current methods, such as patchifying, expedite processes in UNet and Transformer architectures but at the expense of representational capacity. Addressing this, we introduce the Diffusion State Space Model (DiffuSSM), an architecture that supplants attention mechanisms with a more scalable state space model backbone. This approach effectively handles higher resolutions without resorting to global compression, thus preserving detailed image representation throughout the diffusion process. Our focus on FLOP-efficient architectures in diffusion training marks a significant step forward. Comprehensive evaluations on both ImageNet and LSUN datasets at two resolutions demonstrate that DiffuSSMs are on par or even outperform existing diffusion models with attention modules in FID and Inception Score metrics while significantly reducing total FLOP usage.

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.

Generative diffusion models have emerged as a powerful tool for high-quality image synthesis, yet their iterative nature demands significant computational resources. This paper proposes an efficient time step sampling method based on an image spectral analysis of the diffusion process, aimed at optimizing the denoising process. Instead of the traditional uniform distribution-based time step sampling, we introduce a Beta distribution-like sampling technique that prioritizes critical steps in the early and late stages of the process. Our hypothesis is that certain steps exhibit significant changes in image content, while others contribute minimally. We validated our approach using Fourier transforms to measure frequency response changes at each step, revealing substantial low-frequency changes early on and high-frequency adjustments later. Experiments with ADM and Stable Diffusion demonstrated that our Beta Sampling method consistently outperforms uniform sampling, achieving better FID and IS scores, and offers competitive efficiency relative to state-of-the-art methods like AutoDiffusion. This work provides a practical framework for enhancing diffusion model efficiency by focusing computational resources on the most impactful steps, with potential for further optimization and broader application.

While diffusion-based image restoration (IR) methods have achieved remarkable success, they are still limited by the low inference speed attributed to the necessity of executing hundreds or even thousands of sampling steps. Existing acceleration sampling techniques, though seeking to expedite the process, inevitably sacrifice performance to some extent, resulting in over-blurry restored outcomes. To address this issue, this study proposes a novel and efficient diffusion model for IR that significantly reduces the required number of diffusion steps. Our method avoids the need for post-acceleration during inference, thereby avoiding the associated performance deterioration. Specifically, our proposed method establishes a Markov chain that facilitates the transitions between the high-quality and low-quality images by shifting their residuals, substantially improving the transition efficiency. A carefully formulated noise schedule is devised to flexibly control the shifting speed and the noise strength during the diffusion process. Extensive experimental evaluations demonstrate that the proposed method achieves superior or comparable performance to current state-of-the-art methods on three classical IR tasks, namely image super-resolution, image inpainting, and blind face restoration, \textbf{even only with four sampling steps}. Our code and model are publicly available at https://github.com/zsyOAOA/ResShift.

Despite recent advances in inversion-based editing, text-guided image manipulation remains challenging for diffusion models. The primary bottlenecks include 1) the time-consuming nature of the inversion process; 2) the struggle to balance consistency with accuracy; 3) the lack of compatibility with efficient consistency sampling methods used in consistency models. To address the above issues, we start by asking ourselves if the inversion process can be eliminated for editing. We show that when the initial sample is known, a special variance schedule reduces the denoising step to the same form as the multi-step consistency sampling. We name this Denoising Diffusion Consistent Model (DDCM), and note that it implies a virtual inversion strategy without explicit inversion in sampling. We further unify the attention control mechanisms in a tuning-free framework for text-guided editing. Combining them, we present inversion-free editing (InfEdit), which allows for consistent and faithful editing for both rigid and non-rigid semantic changes, catering to intricate modifications without compromising on the image's integrity and explicit inversion. Through extensive experiments, InfEdit shows strong performance in various editing tasks and also maintains a seamless workflow (less than 3 seconds on one single A40), demonstrating the potential for real-time applications. Project Page: https://sled-group.github.io/InfEdit/

Instance segmentation datasets play a crucial role in training accurate and robust computer vision models. However, obtaining accurate mask annotations to produce high-quality segmentation datasets is a costly and labor-intensive process. In this work, we show how this issue can be mitigated by starting with small annotated instance segmentation datasets and augmenting them to effectively obtain a sizeable annotated dataset. We achieve that by creating variations of the available annotated object instances in a way that preserves the provided mask annotations, thereby resulting in new image-mask pairs to be added to the set of annotated images. Specifically, we generate new images using a diffusion-based inpainting model to fill out the masked area with a desired object class by guiding the diffusion through the object outline. We show that the object outline provides a simple, but also reliable and convenient training-free guidance signal for the underlying inpainting model that is often sufficient to fill out the mask with an object of the correct class without further text guidance and preserve the correspondence between generated images and the mask annotations with high precision. Our experimental results reveal that our method successfully generates realistic variations of object instances, preserving their shape characteristics while introducing diversity within the augmented area. We also show that the proposed method can naturally be combined with text guidance and other image augmentation techniques.

There has been a longstanding belief that generation can facilitate a true understanding of visual data. In line with this, we revisit generatively pre-training visual representations in light of recent interest in denoising diffusion models. While directly pre-training with diffusion models does not produce strong representations, we condition diffusion models on masked input and formulate diffusion models as masked autoencoders (DiffMAE). Our approach is capable of (i) serving as a strong initialization for downstream recognition tasks, (ii) conducting high-quality image inpainting, and (iii) being effortlessly extended to video where it produces state-of-the-art classification accuracy. We further perform a comprehensive study on the pros and cons of design choices and build connections between diffusion models and masked autoencoders.

Diffusion models have demonstrated compelling generation quality by optimizing the variational lower bound through a simple denoising score matching loss. In this paper, we provide theoretical evidence that the prevailing practice of using a constant loss weight strategy in diffusion models leads to biased estimation during the training phase. Simply optimizing the denoising network to predict Gaussian noise with constant weighting may hinder precise estimations of original images. To address the issue, we propose an elegant and effective weighting strategy grounded in the theoretically unbiased principle. Moreover, we conduct a comprehensive and systematic exploration to dissect the inherent bias problem deriving from constant weighting loss from the perspectives of its existence, impact and reasons. These analyses are expected to advance our understanding and demystify the inner workings of diffusion models. Through empirical evaluation, we demonstrate that our proposed debiased estimation method significantly enhances sample quality without the reliance on complex techniques, and exhibits improved efficiency compared to the baseline method both in training and sampling processes.

The traditional image inpainting task aims to restore corrupted regions by referencing surrounding background and foreground. However, the object erasure task, which is in increasing demand, aims to erase objects and generate harmonious background. Previous GAN-based inpainting methods struggle with intricate texture generation. Emerging diffusion model-based algorithms, such as Stable Diffusion Inpainting, exhibit the capability to generate novel content, but they often produce incongruent results at the locations of the erased objects and require high-quality text prompt inputs. To address these challenges, we introduce MagicEraser, a diffusion model-based framework tailored for the object erasure task. It consists of two phases: content initialization and controllable generation. In the latter phase, we develop two plug-and-play modules called prompt tuning and semantics-aware attention refocus. Additionally, we propose a data construction strategy that generates training data specially suitable for this task. MagicEraser achieves fine and effective control of content generation while mitigating undesired artifacts. Experimental results highlight a valuable advancement of our approach in the object erasure task.

Diffusion models are emerging expressive generative models, in which a large number of time steps (inference steps) are required for a single image generation. To accelerate such tedious process, reducing steps uniformly is considered as an undisputed principle of diffusion models. We consider that such a uniform assumption is not the optimal solution in practice; i.e., we can find different optimal time steps for different models. Therefore, we propose to search the optimal time steps sequence and compressed model architecture in a unified framework to achieve effective image generation for diffusion models without any further training. Specifically, we first design a unified search space that consists of all possible time steps and various architectures. Then, a two stage evolutionary algorithm is introduced to find the optimal solution in the designed search space. To further accelerate the search process, we employ FID score between generated and real samples to estimate the performance of the sampled examples. As a result, the proposed method is (i).training-free, obtaining the optimal time steps and model architecture without any training process; (ii). orthogonal to most advanced diffusion samplers and can be integrated to gain better sample quality. (iii). generalized, where the searched time steps and architectures can be directly applied on different diffusion models with the same guidance scale. Experimental results show that our method achieves excellent performance by using only a few time steps, e.g. 17.86 FID score on ImageNet 64 times 64 with only four steps, compared to 138.66 with DDIM. The code is available at https://github.com/lilijiangg/AutoDiffusion.

Diffusion models are proficient at generating high-quality images. They are however effective only when operating at the resolution used during training. Inference at a scaled resolution leads to repetitive patterns and structural distortions. Retraining at higher resolutions quickly becomes prohibitive. Thus, methods enabling pre-existing diffusion models to operate at flexible test-time resolutions are highly desirable. Previous works suffer from frequent artifacts and often introduce large latency overheads. We propose two simple modules that combine to solve these issues. We introduce a Frequency Modulation (FM) module that leverages the Fourier domain to improve the global structure consistency, and an Attention Modulation (AM) module which improves the consistency of local texture patterns, a problem largely ignored in prior works. Our method, coined Fam diffusion, can seamlessly integrate into any latent diffusion model and requires no additional training. Extensive qualitative results highlight the effectiveness of our method in addressing structural and local artifacts, while quantitative results show state-of-the-art performance. Also, our method avoids redundant inference tricks for improved consistency such as patch-based or progressive generation, leading to negligible latency overheads.

Diffusion Models (DMs) have empowered great success in artificial-intelligence-generated content, especially in artwork creation, yet raising new concerns in intellectual properties and copyright. For example, infringers can make profits by imitating non-authorized human-created paintings with DMs. Recent researches suggest that various adversarial examples for diffusion models can be effective tools against these copyright infringements. However, current adversarial examples show weakness in transferability over different painting-imitating methods and robustness under straightforward adversarial defense, for example, noise purification. We surprisingly find that the transferability of adversarial examples can be significantly enhanced by exploiting a fused and modified adversarial loss term under consistent parameters. In this work, we comprehensively evaluate the cross-method transferability of adversarial examples. The experimental observation shows that our method generates more transferable adversarial examples with even stronger robustness against the simple adversarial defense.

Diffusion Models have emerged as powerful generative models for high-quality image synthesis, with many subsequent image editing techniques based on them. However, the ease of text-based image editing introduces significant risks, such as malicious editing for scams or intellectual property infringement. Previous works have attempted to safeguard images from diffusion-based editing by adding imperceptible perturbations. These methods are costly and specifically target prevalent Latent Diffusion Models (LDMs), while Pixel-domain Diffusion Models (PDMs) remain largely unexplored and robust against such attacks. Our work addresses this gap by proposing a novel attack framework, AtkPDM. AtkPDM is mainly composed of a feature representation attacking loss that exploits vulnerabilities in denoising UNets and a latent optimization strategy to enhance the naturalness of adversarial images. Extensive experiments demonstrate the effectiveness of our approach in attacking dominant PDM-based editing methods (e.g., SDEdit) while maintaining reasonable fidelity and robustness against common defense methods. Additionally, our framework is extensible to LDMs, achieving comparable performance to existing approaches.

Diffusion models have achieved remarkable success in image and video generation. In this work, we demonstrate that diffusion models can also generate high-performing neural network parameters. Our approach is simple, utilizing an autoencoder and a standard latent diffusion model. The autoencoder extracts latent representations of a subset of the trained network parameters. A diffusion model is then trained to synthesize these latent parameter representations from random noise. It then generates new representations that are passed through the autoencoder's decoder, whose outputs are ready to use as new subsets of network parameters. Across various architectures and datasets, our diffusion process consistently generates models of comparable or improved performance over trained networks, with minimal additional cost. Notably, we empirically find that the generated models perform differently with the trained networks. Our results encourage more exploration on the versatile use of diffusion models.

Diffusion models currently dominate the field of data-driven image synthesis with their unparalleled scaling to large datasets. In this paper, we identify and rectify several causes for uneven and ineffective training in the popular ADM diffusion model architecture, without altering its high-level structure. Observing uncontrolled magnitude changes and imbalances in both the network activations and weights over the course of training, we redesign the network layers to preserve activation, weight, and update magnitudes on expectation. We find that systematic application of this philosophy eliminates the observed drifts and imbalances, resulting in considerably better networks at equal computational complexity. Our modifications improve the previous record FID of 2.41 in ImageNet-512 synthesis to 1.81, achieved using fast deterministic sampling. As an independent contribution, we present a method for setting the exponential moving average (EMA) parameters post-hoc, i.e., after completing the training run. This allows precise tuning of EMA length without the cost of performing several training runs, and reveals its surprising interactions with network architecture, training time, and guidance.

Diffusion models (DMs) have recently gained attention with state-of-the-art performance in text-to-image synthesis. Abiding by the tradition in deep learning, DMs are trained and evaluated on the images with fixed sizes. However, users are demanding for various images with specific sizes and various aspect ratio. This paper focuses on adapting text-to-image diffusion models to handle such variety while maintaining visual fidelity. First we observe that, during the synthesis, lower resolution images suffer from incomplete object portrayal, while higher resolution images exhibit repetitively disordered presentation. Next, we establish a statistical relationship indicating that attention entropy changes with token quantity, suggesting that models aggregate spatial information in proportion to image resolution. The subsequent interpretation on our observations is that objects are incompletely depicted due to limited spatial information for low resolutions, while repetitively disorganized presentation arises from redundant spatial information for high resolutions. From this perspective, we propose a scaling factor to alleviate the change of attention entropy and mitigate the defective pattern observed. Extensive experimental results validate the efficacy of the proposed scaling factor, enabling models to achieve better visual effects, image quality, and text alignment. Notably, these improvements are achieved without additional training or fine-tuning techniques.

Diffusion or flow-based models are powerful generative paradigms that are notoriously hard to sample as samples are defined as solutions to high-dimensional Ordinary or Stochastic Differential Equations (ODEs/SDEs) which require a large Number of Function Evaluations (NFE) to approximate well. Existing methods to alleviate the costly sampling process include model distillation and designing dedicated ODE solvers. However, distillation is costly to train and sometimes can deteriorate quality, while dedicated solvers still require relatively large NFE to produce high quality samples. In this paper we introduce "Bespoke solvers", a novel framework for constructing custom ODE solvers tailored to the ODE of a given pre-trained flow model. Our approach optimizes an order consistent and parameter-efficient solver (e.g., with 80 learnable parameters), is trained for roughly 1% of the GPU time required for training the pre-trained model, and significantly improves approximation and generation quality compared to dedicated solvers. For example, a Bespoke solver for a CIFAR10 model produces samples with Fr\'echet Inception Distance (FID) of 2.73 with 10 NFE, and gets to 1% of the Ground Truth (GT) FID (2.59) for this model with only 20 NFE. On the more challenging ImageNet-64times64, Bespoke samples at 2.2 FID with 10 NFE, and gets within 2% of GT FID (1.71) with 20 NFE.

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives such as human-perceived image quality or drug effectiveness. In this paper, we investigate reinforcement learning methods for directly optimizing diffusion models for such objectives. We describe how posing denoising as a multi-step decision-making problem enables a class of policy gradient algorithms, which we refer to as denoising diffusion policy optimization (DDPO), that are more effective than alternative reward-weighted likelihood approaches. Empirically, DDPO is able to adapt text-to-image diffusion models to objectives that are difficult to express via prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Finally, we show that DDPO can improve prompt-image alignment using feedback from a vision-language model without the need for additional data collection or human annotation.

Material reconstruction from a photograph is a key component of 3D content creation democratization. We propose to formulate this ill-posed problem as a controlled synthesis one, leveraging the recent progress in generative deep networks. We present ControlMat, a method which, given a single photograph with uncontrolled illumination as input, conditions a diffusion model to generate plausible, tileable, high-resolution physically-based digital materials. We carefully analyze the behavior of diffusion models for multi-channel outputs, adapt the sampling process to fuse multi-scale information and introduce rolled diffusion to enable both tileability and patched diffusion for high-resolution outputs. Our generative approach further permits exploration of a variety of materials which could correspond to the input image, mitigating the unknown lighting conditions. We show that our approach outperforms recent inference and latent-space-optimization methods, and carefully validate our diffusion process design choices. Supplemental materials and additional details are available at: https://gvecchio.com/controlmat/.

Audio inpainting refers to the task of reconstructing missing segments in corrupted audio recordings. While prior approaches-including waveform and spectrogram-based diffusion models-have shown promising results for short gaps, they often degrade in quality when gaps exceed 100 milliseconds (ms). In this work, we introduce a novel inpainting method based on discrete diffusion modeling, which operates over tokenized audio representations produced by a pre-trained audio tokenizer. Our approach models the generative process directly in the discrete latent space, enabling stable and semantically coherent reconstruction of missing audio. We evaluate the method on the MusicNet dataset using both objective and perceptual metrics across gap durations up to 300 ms. We further evaluated our approach on the MTG dataset, extending the gap duration to 500 ms. Experimental results demonstrate that our method achieves competitive or superior performance compared to existing baselines, particularly for longer gaps, offering a robust solution for restoring degraded musical recordings. Audio examples of our proposed method can be found at https://iftach21.github.io/

In recent times, the generation of 3D assets from text prompts has shown impressive results. Both 2D and 3D diffusion models can generate decent 3D objects based on prompts. 3D diffusion models have good 3D consistency, but their quality and generalization are limited as trainable 3D data is expensive and hard to obtain. 2D diffusion models enjoy strong abilities of generalization and fine generation, but the 3D consistency is hard to guarantee. This paper attempts to bridge the power from the two types of diffusion models via the recent explicit and efficient 3D Gaussian splatting representation. A fast 3D generation framework, named as \name, is proposed, where the 3D diffusion model provides point cloud priors for initialization and the 2D diffusion model enriches the geometry and appearance. Operations of noisy point growing and color perturbation are introduced to enhance the initialized Gaussians. Our \name can generate a high-quality 3D instance within 25 minutes on one GPU, much faster than previous methods, while the generated instances can be directly rendered in real time. Demos and code are available at https://taoranyi.com/gaussiandreamer/.

The inherent generative power of denoising diffusion models makes them well-suited for image restoration tasks where the objective is to find the optimal high-quality image within the generative space that closely resembles the input image. We propose a method to adapt a pretrained diffusion model for image restoration by simply adding noise to the input image to be restored and then denoise. Our method is based on the observation that the space of a generative model needs to be constrained. We impose this constraint by finetuning the generative model with a set of anchor images that capture the characteristics of the input image. With the constrained space, we can then leverage the sampling strategy used for generation to do image restoration. We evaluate against previous methods and show superior performances on multiple real-world restoration datasets in preserving identity and image quality. We also demonstrate an important and practical application on personalized restoration, where we use a personal album as the anchor images to constrain the generative space. This approach allows us to produce results that accurately preserve high-frequency details, which previous works are unable to do. Project webpage: https://gen2res.github.io.

Diffusion models are the de facto approach for generating high-quality images and videos, but learning high-dimensional models remains a formidable task due to computational and optimization challenges. Existing methods often resort to training cascaded models in pixel space or using a downsampled latent space of a separately trained auto-encoder. In this paper, we introduce Matryoshka Diffusion Models(MDM), an end-to-end framework for high-resolution image and video synthesis. We propose a diffusion process that denoises inputs at multiple resolutions jointly and uses a NestedUNet architecture where features and parameters for small-scale inputs are nested within those of large scales. In addition, MDM enables a progressive training schedule from lower to higher resolutions, which leads to significant improvements in optimization for high-resolution generation. We demonstrate the effectiveness of our approach on various benchmarks, including class-conditioned image generation, high-resolution text-to-image, and text-to-video applications. Remarkably, we can train a single pixel-space model at resolutions of up to 1024x1024 pixels, demonstrating strong zero-shot generalization using the CC12M dataset, which contains only 12 million images.

Because diffusion models have shown impressive performances in a number of tasks, such as image synthesis, there is a trend in recent works to prove (with certain assumptions) that these models have strong approximation capabilities. In this paper, we show that current diffusion models actually have an expressive bottleneck in backward denoising and some assumption made by existing theoretical guarantees is too strong. Based on this finding, we prove that diffusion models have unbounded errors in both local and global denoising. In light of our theoretical studies, we introduce soft mixture denoising (SMD), an expressive and efficient model for backward denoising. SMD not only permits diffusion models to well approximate any Gaussian mixture distributions in theory, but also is simple and efficient for implementation. Our experiments on multiple image datasets show that SMD significantly improves different types of diffusion models (e.g., DDPM), espeically in the situation of few backward iterations.

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

The optimization of the latents and parameters of diffusion models with respect to some differentiable metric defined on the output of the model is a challenging and complex problem. The sampling for diffusion models is done by solving either the probability flow ODE or diffusion SDE wherein a neural network approximates the score function allowing a numerical ODE/SDE solver to be used. However, naive backpropagation techniques are memory intensive, requiring the storage of all intermediate states, and face additional complexity in handling the injected noise from the diffusion term of the diffusion SDE. We propose a novel family of bespoke ODE solvers to the continuous adjoint equations for diffusion models, which we call AdjointDEIS. We exploit the unique construction of diffusion SDEs to further simplify the formulation of the continuous adjoint equations using exponential integrators. Moreover, we provide convergence order guarantees for our bespoke solvers. Significantly, we show that continuous adjoint equations for diffusion SDEs actually simplify to a simple ODE. Lastly, we demonstrate the effectiveness of AdjointDEIS for guided generation with an adversarial attack in the form of the face morphing problem. Our code will be released on our project page https://zblasingame.github.io/AdjointDEIS/

We present a novel approach for generating minority samples that live on low-density regions of a data manifold. Our framework is built upon diffusion models, leveraging the principle of guided sampling that incorporates an arbitrary energy-based guidance during inference time. The key defining feature of our sampler lies in its self-contained nature, \ie, implementable solely with a pretrained model. This distinguishes our sampler from existing techniques that require expensive additional components (like external classifiers) for minority generation. Specifically, we first estimate the likelihood of features within an intermediate latent sample by evaluating a reconstruction loss w.r.t. its posterior mean. The generation then proceeds with the minimization of the estimated likelihood, thereby encouraging the emergence of minority features in the latent samples of subsequent timesteps. To further improve the performance of our sampler, we provide several time-scheduling techniques that properly manage the influence of guidance over inference steps. Experiments on benchmark real datasets demonstrate that our approach can greatly improve the capability of creating realistic low-likelihood minority instances over the existing techniques without the reliance on costly additional elements. Code is available at https://github.com/soobin-um/sg-minority.

Diffusion frameworks have achieved comparable performance with previous state-of-the-art image generation models. Researchers are curious about its variants in discriminative tasks because of its powerful noise-to-image denoising pipeline. This paper proposes DiffusionInst, a novel framework that represents instances as instance-aware filters and formulates instance segmentation as a noise-to-filter denoising process. The model is trained to reverse the noisy groundtruth without any inductive bias from RPN. During inference, it takes a randomly generated filter as input and outputs mask in one-step or multi-step denoising. Extensive experimental results on COCO and LVIS show that DiffusionInst achieves competitive performance compared to existing instance segmentation models with various backbones, such as ResNet and Swin Transformers. We hope our work could serve as a strong baseline, which could inspire designing more efficient diffusion frameworks for challenging discriminative tasks. Our code is available in https://github.com/chenhaoxing/DiffusionInst.

Image inpainting refers to the task of generating a complete, natural image based on a partially revealed reference image. Recently, many research interests have been focused on addressing this problem using fixed diffusion models. These approaches typically directly replace the revealed region of the intermediate or final generated images with that of the reference image or its variants. However, since the unrevealed regions are not directly modified to match the context, it results in incoherence between revealed and unrevealed regions. To address the incoherence problem, a small number of methods introduce a rigorous Bayesian framework, but they tend to introduce mismatches between the generated and the reference images due to the approximation errors in computing the posterior distributions. In this paper, we propose COPAINT, which can coherently inpaint the whole image without introducing mismatches. COPAINT also uses the Bayesian framework to jointly modify both revealed and unrevealed regions, but approximates the posterior distribution in a way that allows the errors to gradually drop to zero throughout the denoising steps, thus strongly penalizing any mismatches with the reference image. Our experiments verify that COPAINT can outperform the existing diffusion-based methods under both objective and subjective metrics. The codes are available at https://github.com/UCSB-NLP-Chang/CoPaint/.

Neural Radiance Field (NeRF) is a representation for 3D reconstruction from multi-view images. Despite some recent work showing preliminary success in editing a reconstructed NeRF with diffusion prior, they remain struggling to synthesize reasonable geometry in completely uncovered regions. One major reason is the high diversity of synthetic contents from the diffusion model, which hinders the radiance field from converging to a crisp and deterministic geometry. Moreover, applying latent diffusion models on real data often yields a textural shift incoherent to the image condition due to auto-encoding errors. These two problems are further reinforced with the use of pixel-distance losses. To address these issues, we propose tempering the diffusion model's stochasticity with per-scene customization and mitigating the textural shift with masked adversarial training. During the analyses, we also found the commonly used pixel and perceptual losses are harmful in the NeRF inpainting task. Through rigorous experiments, our framework yields state-of-the-art NeRF inpainting results on various real-world scenes. Project page: https://hubert0527.github.io/MALD-NeRF

Recently, using diffusion models for zero-shot image restoration (IR) has become a new hot paradigm. This type of method only needs to use the pre-trained off-the-shelf diffusion models, without any finetuning, and can directly handle various IR tasks. The upper limit of the restoration performance depends on the pre-trained diffusion models, which are in rapid evolution. However, current methods only discuss how to deal with fixed-size images, but dealing with images of arbitrary sizes is very important for practical applications. This paper focuses on how to use those diffusion-based zero-shot IR methods to deal with any size while maintaining the excellent characteristics of zero-shot. A simple way to solve arbitrary size is to divide it into fixed-size patches and solve each patch independently. But this may yield significant artifacts since it neither considers the global semantics of all patches nor the local information of adjacent patches. Inspired by the Range-Null space Decomposition, we propose the Mask-Shift Restoration to address local incoherence and propose the Hierarchical Restoration to alleviate out-of-domain issues. Our simple, parameter-free approaches can be used not only for image restoration but also for image generation of unlimited sizes, with the potential to be a general tool for diffusion models. Code: https://github.com/wyhuai/DDNM/tree/main/hq_demo

Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing boldsymbol v-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

Diffusion (score-based) generative models have been widely used for modeling various types of complex data, including images, audios, and point clouds. Recently, the deep connection between forward-backward stochastic differential equations (SDEs) and diffusion-based models has been revealed, and several new variants of SDEs are proposed (e.g., sub-VP, critically-damped Langevin) along this line. Despite the empirical success of the hand-crafted fixed forward SDEs, a great quantity of proper forward SDEs remain unexplored. In this work, we propose a general framework for parameterizing the diffusion model, especially the spatial part of the forward SDE. An abstract formalism is introduced with theoretical guarantees, and its connection with previous diffusion models is leveraged. We demonstrate the theoretical advantage of our method from an optimization perspective. Numerical experiments on synthetic datasets, MINIST and CIFAR10 are also presented to validate the effectiveness of our framework.

Diffusion models excel in high-quality generation but suffer from slow inference due to iterative sampling. While recent methods have successfully transformed diffusion models into one-step generators, they neglect model size reduction, limiting their applicability in compute-constrained scenarios. This paper aims to develop small, efficient one-step diffusion models based on the powerful rectified flow framework, by exploring joint compression of inference steps and model size. The rectified flow framework trains one-step generative models using two operations, reflow and distillation. Compared with the original framework, squeezing the model size brings two new challenges: (1) the initialization mismatch between large teachers and small students during reflow; (2) the underperformance of naive distillation on small student models. To overcome these issues, we propose Annealing Reflow and Flow-Guided Distillation, which together comprise our SlimFlow framework. With our novel framework, we train a one-step diffusion model with an FID of 5.02 and 15.7M parameters, outperforming the previous state-of-the-art one-step diffusion model (FID=6.47, 19.4M parameters) on CIFAR10. On ImageNet 64times64 and FFHQ 64times64, our method yields small one-step diffusion models that are comparable to larger models, showcasing the effectiveness of our method in creating compact, efficient one-step diffusion models.

Recent surge in large-scale generative models has spurred the development of vast fields in computer vision. In particular, text-to-image diffusion models have garnered widespread adoption across diverse domain due to their potential for high-fidelity image generation. Nonetheless, existing large-scale diffusion models are confined to generate images of up to 1K resolution, which is far from meeting the demands of contemporary commercial applications. Directly sampling higher-resolution images often yields results marred by artifacts such as object repetition and distorted shapes. Addressing the aforementioned issues typically necessitates training or fine-tuning models on higher resolution datasets. However, this undertaking poses a formidable challenge due to the difficulty in collecting large-scale high-resolution contents and substantial computational resources. While several preceding works have proposed alternatives, they often fail to produce convincing results. In this work, we probe the generative ability of diffusion models at higher resolution beyond its original capability and propose a novel progressive approach that fully utilizes generated low-resolution image to guide the generation of higher resolution image. Our method obviates the need for additional training or fine-tuning which significantly lowers the burden of computational costs. Extensive experiments and results validate the efficiency and efficacy of our method. Project page: https://yhyun225.github.io/DiffuseHigh/

Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which uses a single pre-training stage to address both families of tasks simultaneously. We identify diffusion models as a prime candidate. Diffusion models have risen to prominence as a state-of-the-art method for image generation, denoising, inpainting, super-resolution, manipulation, etc. Such models involve training a U-Net to iteratively predict and remove noise, and the resulting model can synthesize high fidelity, diverse, novel images. The U-Net architecture, as a convolution-based architecture, generates a diverse set of feature representations in the form of intermediate feature maps. We present our findings that these embeddings are useful beyond the noise prediction task, as they contain discriminative information and can also be leveraged for classification. We explore optimal methods for extracting and using these embeddings for classification tasks, demonstrating promising results on the ImageNet classification task. We find that with careful feature selection and pooling, diffusion models outperform comparable generative-discriminative methods such as BigBiGAN for classification tasks. We investigate diffusion models in the transfer learning regime, examining their performance on several fine-grained visual classification datasets. We compare these embeddings to those generated by competing architectures and pre-trainings for classification tasks.

In recent years, masked diffusion models (MDMs) have emerged as a promising alternative approach for generative modeling over discrete domains. Compared to autoregressive models (ARMs), MDMs trade off complexity at training time with flexibility at inference time. At training time, they must learn to solve an exponentially large number of infilling problems, but at inference time, they can decode tokens in essentially arbitrary order. In this work, we closely examine these two competing effects. On the training front, we theoretically and empirically demonstrate that MDMs indeed train on computationally intractable subproblems compared to their autoregressive counterparts. On the inference front, we show that a suitable strategy for adaptively choosing the token decoding order significantly enhances the capabilities of MDMs, allowing them to sidestep hard subproblems. On logic puzzles like Sudoku, we show that adaptive inference can boost solving accuracy in pretrained MDMs from <7% to approx 90%, even outperforming ARMs with 7times as many parameters and that were explicitly trained via teacher forcing to learn the right order of decoding.

In this paper, we point out suboptimal noise-data mapping leads to slow training of diffusion models. During diffusion training, current methods diffuse each image across the entire noise space, resulting in a mixture of all images at every point in the noise layer. We emphasize that this random mixture of noise-data mapping complicates the optimization of the denoising function in diffusion models. Drawing inspiration from the immiscible phenomenon in physics, we propose Immiscible Diffusion, a simple and effective method to improve the random mixture of noise-data mapping. In physics, miscibility can vary according to various intermolecular forces. Thus, immiscibility means that the mixing of the molecular sources is distinguishable. Inspired by this, we propose an assignment-then-diffusion training strategy. Specifically, prior to diffusing the image data into noise, we assign diffusion target noise for the image data by minimizing the total image-noise pair distance in a mini-batch. The assignment functions analogously to external forces to separate the diffuse-able areas of images, thus mitigating the inherent difficulties in diffusion training. Our approach is remarkably simple, requiring only one line of code to restrict the diffuse-able area for each image while preserving the Gaussian distribution of noise. This ensures that each image is projected only to nearby noise. To address the high complexity of the assignment algorithm, we employ a quantized-assignment method to reduce the computational overhead to a negligible level. Experiments demonstrate that our method achieve up to 3x faster training for consistency models and DDIM on the CIFAR dataset, and up to 1.3x faster on CelebA datasets for consistency models. Besides, we conduct thorough analysis about the Immiscible Diffusion, which sheds lights on how it improves diffusion training speed while improving the fidelity.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality. However, the editing performance of diffusion models tends to be no more satisfactory even with increasing denoising steps. The deficiency in editing could be attributed to the conditional Markovian property of the editing process, where errors accumulate throughout denoising steps. To tackle this challenge, we first propose an innovative framework where a rectifier module is incorporated to modulate diffusion model weights with residual features, thereby providing compensatory information to bridge the fidelity gap. Furthermore, we introduce a novel learning paradigm aimed at minimizing error propagation during the editing process, which trains the editing procedure in a manner similar to denoising score-matching. Extensive experiments demonstrate that our proposed framework and training strategy achieve high-fidelity reconstruction and editing results across various levels of denoising steps, meanwhile exhibits exceptional performance in terms of both quantitative metric and qualitative assessments. Moreover, we explore our model's generalization through several applications like image-to-image translation and out-of-domain image editing.

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed point solving layer into the denoising network of a diffusion model, transforming the diffusion process into a sequence of closely-related fixed point problems. Combined with a new stochastic training method, this approach significantly reduces model size, reduces memory usage, and accelerates training. Moreover, it enables the development of two new techniques to improve sampling efficiency: reallocating computation across timesteps and reusing fixed point solutions between timesteps. We conduct extensive experiments with state-of-the-art models on ImageNet, FFHQ, CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in performance and efficiency. Compared to the state-of-the-art DiT model, FPDM contains 87% fewer parameters, consumes 60% less memory during training, and improves image generation quality in situations where sampling computation or time is limited. Our code and pretrained models are available at https://lukemelas.github.io/fixed-point-diffusion-models.

Diffusion models have shown great promise in synthesizing visually appealing images. However, it remains challenging to condition the synthesis at a fine-grained level, for instance, synthesizing image pixels following some generic color pattern. Existing image synthesis methods often produce contents that fall outside the desired pixel conditions. To address this, we introduce a novel color alignment algorithm that confines the generative process in diffusion models within a given color pattern. Specifically, we project diffusion terms, either imagery samples or latent representations, into a conditional color space to align with the input color distribution. This strategy simplifies the prediction in diffusion models within a color manifold while still allowing plausible structures in generated contents, thus enabling the generation of diverse contents that comply with the target color pattern. Experimental results demonstrate our state-of-the-art performance in conditioning and controlling of color pixels, while maintaining on-par generation quality and diversity in comparison with regular diffusion models.

Diffusion Morphs (DiM) are a recent state-of-the-art method for creating high quality face morphs; however, they require a high number of network function evaluations (NFE) to create the morphs. We propose a new DiM pipeline, Fast-DiM, which can create morphs of a similar quality but with fewer NFE. We investigate the ODE solvers used to solve the Probability Flow ODE and the impact they have on the the creation of face morphs. Additionally, we employ an alternative method for encoding images into the latent space of the Diffusion model by solving the Probability Flow ODE as time runs forwards. Our experiments show that we can reduce the NFE by upwards of 85% in the encoding process while experiencing only 1.6\% reduction in Mated Morph Presentation Match Rate (MMPMR). Likewise, we showed we could cut NFE, in the sampling process, in half with only a maximal reduction of 0.23% in MMPMR.

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired image-to-image (I2I) translation tasks due to the Gaussian prior assumption. Schr\"{o}dinger Bridge (SB), which learns an SDE to translate between two arbitrary distributions, have risen as an attractive solution to this problem. Yet, to our best knowledge, none of SB models so far have been successful at unpaired translation between high-resolution images. In this work, we propose Unpaired Neural Schr\"{o}dinger Bridge (UNSB), which expresses the SB problem as a sequence of adversarial learning problems. This allows us to incorporate advanced discriminators and regularization to learn a SB between unpaired data. We show that UNSB is scalable and successfully solves various unpaired I2I translation tasks. Code: https://github.com/cyclomon/UNSB

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that the same noise level on a higher resolution results in a higher Signal-to-Noise Ratio in the frequency domain. In this work, we present Relay Diffusion Model (RDM), which transfers a low-resolution image or noise into an equivalent high-resolution one for diffusion model via blurring diffusion and block noise. Therefore, the diffusion process can continue seamlessly in any new resolution or model without restarting from pure noise or low-resolution conditioning. RDM achieves state-of-the-art FID on CelebA-HQ and sFID on ImageNet 256times256, surpassing previous works such as ADM, LDM and DiT by a large margin. All the codes and checkpoints are open-sourced at https://github.com/THUDM/RelayDiffusion.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem in many applications of partial differential equations (PDEs). The main novelty of the proposed dataset is that we consider discontinuous coefficients with high contrast. These coefficient functions are sampled from a selected set of distributions. This class of problems is not only of great academic interest, but is also the basis for describing various environmental and industrial problems. In this way, ConDiff shortens the gap with real-world problems while remaining fully synthetic and easy to use. ConDiff consists of a diverse set of diffusion equations with coefficients covering a wide range of contrast levels and heterogeneity with a measurable complexity metric for clearer comparison between different coefficient functions. We baseline ConDiff on standard deep learning models in the field of scientific machine learning. By providing a large number of problem instances, each with its own coefficient function and right-hand side, we hope to encourage the development of novel physics-based deep learning approaches, such as neural operators, ultimately driving progress towards more accurate and efficient solutions of complex PDE problems.

Diffusion models have quickly become the state-of-the-art for generation tasks across many different data modalities. An important ability of diffusion models is the ability to encode samples from the data distribution back into the sampling prior distribution. This is useful for performing alterations to real data samples along with guided generation via the continuous adjoint equations. We propose an algebraically reversible solver for diffusion SDEs that can exactly invert real data samples into the prior distribution.

We introduce a theoretical framework for diffusion-based image editing by formulating it as a reverse-time bridge modeling problem. This approach modifies the backward process of a pretrained diffusion model to construct a bridge that converges to an implicit distribution associated with the editing target at time 0. Building on this framework, we propose h-Edit, a novel editing method that utilizes Doob's h-transform and Langevin Monte Carlo to decompose the update of an intermediate edited sample into two components: a "reconstruction" term and an "editing" term. This decomposition provides flexibility, allowing the reconstruction term to be computed via existing inversion techniques and enabling the combination of multiple editing terms to handle complex editing tasks. To our knowledge, h-Edit is the first training-free method capable of performing simultaneous text-guided and reward-model-based editing. Extensive experiments, both quantitative and qualitative, show that h-Edit outperforms state-of-the-art baselines in terms of editing effectiveness and faithfulness. Our source code is available at https://github.com/nktoan/h-edit.

Diffusion models suffer from slow sample generation at inference time. Therefore, developing a principled framework for fast deterministic/stochastic sampling for a broader class of diffusion models is a promising direction. We propose two complementary frameworks for accelerating sample generation in pre-trained models: Conjugate Integrators and Splitting Integrators. Conjugate integrators generalize DDIM, mapping the reverse diffusion dynamics to a more amenable space for sampling. In contrast, splitting-based integrators, commonly used in molecular dynamics, reduce the numerical simulation error by cleverly alternating between numerical updates involving the data and auxiliary variables. After extensively studying these methods empirically and theoretically, we present a hybrid method that leads to the best-reported performance for diffusion models in augmented spaces. Applied to Phase Space Langevin Diffusion [Pandey & Mandt, 2023] on CIFAR-10, our deterministic and stochastic samplers achieve FID scores of 2.11 and 2.36 in only 100 network function evaluations (NFE) as compared to 2.57 and 2.63 for the best-performing baselines, respectively. Our code and model checkpoints will be made publicly available at https://github.com/mandt-lab/PSLD.

The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate 50k images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis

Compositing an object into an image involves multiple non-trivial sub-tasks such as object placement and scaling, color/lighting harmonization, viewpoint/geometry adjustment, and shadow/reflection generation. Recent generative image compositing methods leverage diffusion models to handle multiple sub-tasks at once. However, existing models face limitations due to their reliance on masking the original object during training, which constrains their generation to the input mask. Furthermore, obtaining an accurate input mask specifying the location and scale of the object in a new image can be highly challenging. To overcome such limitations, we define a novel problem of unconstrained generative object compositing, i.e., the generation is not bounded by the mask, and train a diffusion-based model on a synthesized paired dataset. Our first-of-its-kind model is able to generate object effects such as shadows and reflections that go beyond the mask, enhancing image realism. Additionally, if an empty mask is provided, our model automatically places the object in diverse natural locations and scales, accelerating the compositing workflow. Our model outperforms existing object placement and compositing models in various quality metrics and user studies.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Over the past decade, there has been tremendous progress in the domain of synthetic media generation. This is mainly due to the powerful methods based on generative adversarial networks (GANs). Very recently, diffusion probabilistic models, which are inspired by non-equilibrium thermodynamics, have taken the spotlight. In the realm of image generation, diffusion models (DMs) have exhibited remarkable proficiency in producing both realistic and heterogeneous imagery through their stochastic sampling procedure. This paper proposes a novel facial swapping module, termed as LDFaceNet (Latent Diffusion based Face Swapping Network), which is based on a guided latent diffusion model that utilizes facial segmentation and facial recognition modules for a conditioned denoising process. The model employs a unique loss function to offer directional guidance to the diffusion process. Notably, LDFaceNet can incorporate supplementary facial guidance for desired outcomes without any retraining. To the best of our knowledge, this represents the first application of the latent diffusion model in the face-swapping task without prior training. The results of this study demonstrate that the proposed method can generate extremely realistic and coherent images by leveraging the potential of the diffusion model for facial swapping, thereby yielding superior visual outcomes and greater diversity.

Diffusion models have emerged as dominant performers for image generation. To support training large diffusion models, this paper studies pipeline parallel training of diffusion models and proposes DiffusionPipe, a synchronous pipeline training system that advocates innovative pipeline bubble filling technique, catering to structural characteristics of diffusion models. State-of-the-art diffusion models typically include trainable (the backbone) and non-trainable (e.g., frozen input encoders) parts. We first unify optimal stage partitioning and pipeline scheduling of single and multiple backbones in representative diffusion models with a dynamic programming approach. We then propose to fill the computation of non-trainable model parts into idle periods of the pipeline training of the backbones by an efficient greedy algorithm, thus achieving high training throughput. Extensive experiments show that DiffusionPipe can achieve up to 1.41x speedup over pipeline parallel methods and 1.28x speedup over data parallel training on popular diffusion models.

Voice conversion is a common speech synthesis task which can be solved in different ways depending on a particular real-world scenario. The most challenging one often referred to as one-shot many-to-many voice conversion consists in copying the target voice from only one reference utterance in the most general case when both source and target speakers do not belong to the training dataset. We present a scalable high-quality solution based on diffusion probabilistic modeling and demonstrate its superior quality compared to state-of-the-art one-shot voice conversion approaches. Moreover, focusing on real-time applications, we investigate general principles which can make diffusion models faster while keeping synthesis quality at a high level. As a result, we develop a novel Stochastic Differential Equations solver suitable for various diffusion model types and generative tasks as shown through empirical studies and justify it by theoretical analysis.