Daily Papers

Diffusion-based voice conversion (VC) techniques such as VoiceGrad have attracted interest because of their high VC performance in terms of speech quality and speaker similarity. However, a notable limitation is the slow inference caused by the multi-step reverse diffusion. Therefore, we propose FastVoiceGrad, a novel one-step diffusion-based VC that reduces the number of iterations from dozens to one while inheriting the high VC performance of the multi-step diffusion-based VC. We obtain the model using adversarial conditional diffusion distillation (ACDD), leveraging the ability of generative adversarial networks and diffusion models while reconsidering the initial states in sampling. Evaluations of one-shot any-to-any VC demonstrate that FastVoiceGrad achieves VC performance superior to or comparable to that of previous multi-step diffusion-based VC while enhancing the inference speed. Audio samples are available at https://www.kecl.ntt.co.jp/people/kaneko.takuhiro/projects/fastvoicegrad/.

Diffusion models have demonstrated their effectiveness across various generative tasks. However, when applied to medical image segmentation, these models encounter several challenges, including significant resource and time requirements. They also necessitate a multi-step reverse process and multiple samples to produce reliable predictions. To address these challenges, we introduce the first latent diffusion segmentation model, named SDSeg, built upon stable diffusion (SD). SDSeg incorporates a straightforward latent estimation strategy to facilitate a single-step reverse process and utilizes latent fusion concatenation to remove the necessity for multiple samples. Extensive experiments indicate that SDSeg surpasses existing state-of-the-art methods on five benchmark datasets featuring diverse imaging modalities. Remarkably, SDSeg is capable of generating stable predictions with a solitary reverse step and sample, epitomizing the model's stability as implied by its name. The code is available at https://github.com/lin-tianyu/Stable-Diffusion-Seg

Recent advances in text-to-image (T2I) diffusion models have facilitated creative and photorealistic image synthesis. By varying the random seeds, we can generate various images for a fixed text prompt. Technically, the seed controls the initial noise and, in multi-step diffusion inference, the noise used for reparameterization at intermediate timesteps in the reverse diffusion process. However, the specific impact of the random seed on the generated images remains relatively unexplored. In this work, we conduct a large-scale scientific study into the impact of random seeds during diffusion inference. Remarkably, we reveal that the best 'golden' seed achieved an impressive FID of 21.60, compared to the worst 'inferior' seed's FID of 31.97. Additionally, a classifier can predict the seed number used to generate an image with over 99.9% accuracy in just a few epochs, establishing that seeds are highly distinguishable based on generated images. Encouraged by these findings, we examined the influence of seeds on interpretable visual dimensions. We find that certain seeds consistently produce grayscale images, prominent sky regions, or image borders. Seeds also affect image composition, including object location, size, and depth. Moreover, by leveraging these 'golden' seeds, we demonstrate improved image generation such as high-fidelity inference and diversified sampling. Our investigation extends to inpainting tasks, where we uncover some seeds that tend to insert unwanted text artifacts. Overall, our extensive analyses highlight the importance of selecting good seeds and offer practical utility for image generation.

Recent progress in 3D reconstruction has enabled realistic 3D models from dense image captures, yet challenges persist with sparse views, often leading to artifacts in unseen areas. Recent works leverage Video Diffusion Models (VDMs) to generate dense observations, filling the gaps when only sparse views are available for 3D reconstruction tasks. A significant limitation of these methods is their slow sampling speed when using VDMs. In this paper, we present FVGen, a novel framework that addresses this challenge by enabling fast novel view synthesis using VDMs in as few as four sampling steps. We propose a novel video diffusion model distillation method that distills a multi-step denoising teacher model into a few-step denoising student model using Generative Adversarial Networks (GANs) and softened reverse KL-divergence minimization. Extensive experiments on real-world datasets show that, compared to previous works, our framework generates the same number of novel views with similar (or even better) visual quality while reducing sampling time by more than 90%. FVGen significantly improves time efficiency for downstream reconstruction tasks, particularly when working with sparse input views (more than 2) where pre-trained VDMs need to be run multiple times to achieve better spatial coverage.

Diffusion models are trained by learning a sequence of models that reverse each step of noise corruption. Typically, the model parameters are fully shared across multiple timesteps to enhance training efficiency. However, since the denoising tasks differ at each timestep, the gradients computed at different timesteps may conflict, potentially degrading the overall performance of image generation. To solve this issue, this work proposes a Decouple-then-Merge (DeMe) framework, which begins with a pretrained model and finetunes separate models tailored to specific timesteps. We introduce several improved techniques during the finetuning stage to promote effective knowledge sharing while minimizing training interference across timesteps. Finally, after finetuning, these separate models can be merged into a single model in the parameter space, ensuring efficient and practical inference. Experimental results show significant generation quality improvements upon 6 benchmarks including Stable Diffusion on COCO30K, ImageNet1K, PartiPrompts, and DDPM on LSUN Church, LSUN Bedroom, and CIFAR10. Code is available at https://github.com/MqLeet/DeMe{GitHub}.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

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

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.

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.

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.

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.

Denoising diffusion models (DDMs) have led to staggering performance leaps in image generation, editing and restoration. However, existing DDMs use very large datasets for training. Here, we introduce a framework for training a DDM on a single image. Our method, which we coin SinDDM, learns the internal statistics of the training image by using a multi-scale diffusion process. To drive the reverse diffusion process, we use a fully-convolutional light-weight denoiser, which is conditioned on both the noise level and the scale. This architecture allows generating samples of arbitrary dimensions, in a coarse-to-fine manner. As we illustrate, SinDDM generates diverse high-quality samples, and is applicable in a wide array of tasks, including style transfer and harmonization. Furthermore, it can be easily guided by external supervision. Particularly, we demonstrate text-guided generation from a single image using a pre-trained CLIP model.

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.

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.

Diffusion distillation models effectively accelerate reverse sampling by compressing the process into fewer steps. However, these models still exhibit a performance gap compared to their pre-trained diffusion model counterparts, exacerbated by distribution shifts and accumulated errors during multi-step sampling. To address this, we introduce Distillation++, a novel inference-time distillation framework that reduces this gap by incorporating teacher-guided refinement during sampling. Inspired by recent advances in conditional sampling, our approach recasts student model sampling as a proximal optimization problem with a score distillation sampling loss (SDS). To this end, we integrate distillation optimization during reverse sampling, which can be viewed as teacher guidance that drives student sampling trajectory towards the clean manifold using pre-trained diffusion models. Thus, Distillation++ improves the denoising process in real-time without additional source data or fine-tuning. Distillation++ demonstrates substantial improvements over state-of-the-art distillation baselines, particularly in early sampling stages, positioning itself as a robust guided sampling process crafted for diffusion distillation models. Code: https://github.com/geonyeong-park/inference_distillation.

We address the challenges of precise image inversion and disentangled image editing in the context of few-step diffusion models. We introduce an encoder based iterative inversion technique. The inversion network is conditioned on the input image and the reconstructed image from the previous step, allowing for correction of the next reconstruction towards the input image. We demonstrate that disentangled controls can be easily achieved in the few-step diffusion model by conditioning on an (automatically generated) detailed text prompt. To manipulate the inverted image, we freeze the noise maps and modify one attribute in the text prompt (either manually or via instruction based editing driven by an LLM), resulting in the generation of a new image similar to the input image with only one attribute changed. It can further control the editing strength and accept instructive text prompt. Our approach facilitates realistic text-guided image edits in real-time, requiring only 8 number of functional evaluations (NFEs) in inversion (one-time cost) and 4 NFEs per edit. Our method is not only fast, but also significantly outperforms state-of-the-art multi-step diffusion editing techniques.

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems. For example, we achieve a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, which is an improvement of 9.12dB compared to 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 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.

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that recovers the data distribution from time-dependent data scores. In this work, we observe that the stochastic reverse process of data scores is a martingale, from which concentration bounds and the optional stopping theorem for data scores can be derived. Then, we discover a simple way for calibrating an arbitrary pretrained DPM, with which the score matching loss can be reduced and the lower bounds of model likelihood can consequently be increased. We provide general calibration guidelines under various model parametrizations. Our calibration method is performed only once and the resulting models can be used repeatedly for sampling. We conduct experiments on multiple datasets to empirically validate our proposal. Our code is at https://github.com/thudzj/Calibrated-DPMs.

Diffusion models have revolutionized text-to-image generation with its exceptional quality and creativity. However, its multi-step sampling process is known to be slow, often requiring tens of inference steps to obtain satisfactory results. Previous attempts to improve its sampling speed and reduce computational costs through distillation have been unsuccessful in achieving a functional one-step model. In this paper, we explore a recent method called Rectified Flow, which, thus far, has only been applied to small datasets. The core of Rectified Flow lies in its reflow procedure, which straightens the trajectories of probability flows, refines the coupling between noises and images, and facilitates the distillation process with student models. We propose a novel text-conditioned pipeline to turn Stable Diffusion (SD) into an ultra-fast one-step model, in which we find reflow plays a critical role in improving the assignment between noise and images. Leveraging our new pipeline, we create, to the best of our knowledge, the first one-step diffusion-based text-to-image generator with SD-level image quality, achieving an FID (Frechet Inception Distance) of 23.3 on MS COCO 2017-5k, surpassing the previous state-of-the-art technique, progressive distillation, by a significant margin (37.2 rightarrow 23.3 in FID). By utilizing an expanded network with 1.7B parameters, we further improve the FID to 22.4. We call our one-step models InstaFlow. On MS COCO 2014-30k, InstaFlow yields an FID of 13.1 in just 0.09 second, the best in leq 0.1 second regime, outperforming the recent StyleGAN-T (13.9 in 0.1 second). Notably, the training of InstaFlow only costs 199 A100 GPU days. Project page:~https://github.com/gnobitab/InstaFlow.

Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs and GANs cover the target distribution. Finally, we show that the sample quality and likelihood of these models scale smoothly with model capacity and training compute, making them easily scalable. We release our code at https://github.com/openai/improved-diffusion

We address the problem of synthesizing multi-view optical illusions: images that change appearance upon a transformation, such as a flip or rotation. We propose a simple, zero-shot method for obtaining these illusions from off-the-shelf text-to-image diffusion models. During the reverse diffusion process, we estimate the noise from different views of a noisy image, and then combine these noise estimates together and denoise the image. A theoretical analysis suggests that this method works precisely for views that can be written as orthogonal transformations, of which permutations are a subset. This leads to the idea of a visual anagram--an image that changes appearance under some rearrangement of pixels. This includes rotations and flips, but also more exotic pixel permutations such as a jigsaw rearrangement. Our approach also naturally extends to illusions with more than two views. We provide both qualitative and quantitative results demonstrating the effectiveness and flexibility of our method. Please see our project webpage for additional visualizations and results: https://dangeng.github.io/visual_anagrams/

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

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.

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

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 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.

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.

Diffusion-based generative modeling has been achieving state-of-the-art results on various generation tasks. Most diffusion models, however, are limited to a single-generation modeling. Can we generalize diffusion models with the ability of multi-modal generative training for more generalizable modeling? In this paper, we propose a principled way to define a diffusion model by constructing a unified multi-modal diffusion model in a common diffusion space. We define the forward diffusion process to be driven by an information aggregation from multiple types of task-data, e.g., images for a generation task and labels for a classification task. In the reverse process, we enforce information sharing by parameterizing a shared backbone denoising network with additional modality-specific decoder heads. Such a structure can simultaneously learn to generate different types of multi-modal data with a multi-task loss, which is derived from a new multi-modal variational lower bound that generalizes the standard diffusion model. We propose several multimodal generation settings to verify our framework, including image transition, masked-image training, joint image-label and joint image-representation generative modeling. Extensive experimental results on ImageNet indicate the effectiveness of our framework for various multi-modal generative modeling, which we believe is an important research direction worthy of more future explorations.

Diffusion models are a powerful generative framework, but come with expensive inference. Existing acceleration methods often compromise image quality or fail under complex conditioning when operating in an extremely low-step regime. In this work, we propose a novel distillation framework tailored to enable high-fidelity, diverse sample generation using just one to three steps. Our approach comprises three key components: (i) Backward Distillation, which mitigates training-inference discrepancies by calibrating the student on its own backward trajectory; (ii) Shifted Reconstruction Loss that dynamically adapts knowledge transfer based on the current time step; and (iii) Noise Correction, an inference-time technique that enhances sample quality by addressing singularities in noise prediction. Through extensive experiments, we demonstrate that our method outperforms existing competitors in quantitative metrics and human evaluations. Remarkably, it achieves performance comparable to the teacher model using only three denoising steps, enabling efficient high-quality generation.

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.

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

The development of video diffusion models unveils a significant challenge: the substantial computational demands. To mitigate this challenge, we note that the reverse process of diffusion exhibits an inherent entropy-reducing nature. Given the inter-frame redundancy in video modality, maintaining full frame rates in high-entropy stages is unnecessary. Based on this insight, we propose TPDiff, a unified framework to enhance training and inference efficiency. By dividing diffusion into several stages, our framework progressively increases frame rate along the diffusion process with only the last stage operating on full frame rate, thereby optimizing computational efficiency. To train the multi-stage diffusion model, we introduce a dedicated training framework: stage-wise diffusion. By solving the partitioned probability flow ordinary differential equations (ODE) of diffusion under aligned data and noise, our training strategy is applicable to various diffusion forms and further enhances training efficiency. Comprehensive experimental evaluations validate the generality of our method, demonstrating 50% reduction in training cost and 1.5x improvement in inference efficiency.

Existing single image-to-3D creation methods typically involve a two-stage process, first generating multi-view images, and then using these images for 3D reconstruction. However, training these two stages separately leads to significant data bias in the inference phase, thus affecting the quality of reconstructed results. We introduce a unified 3D generation framework, named Ouroboros3D, which integrates diffusion-based multi-view image generation and 3D reconstruction into a recursive diffusion process. In our framework, these two modules are jointly trained through a self-conditioning mechanism, allowing them to adapt to each other's characteristics for robust inference. During the multi-view denoising process, the multi-view diffusion model uses the 3D-aware maps rendered by the reconstruction module at the previous timestep as additional conditions. The recursive diffusion framework with 3D-aware feedback unites the entire process and improves geometric consistency.Experiments show that our framework outperforms separation of these two stages and existing methods that combine them at the inference phase. Project page: https://costwen.github.io/Ouroboros3D/

An increasing number of autoregressive models, such as MAR, FlowAR, xAR, and Harmon adopt diffusion sampling to improve the quality of image generation. However, this strategy leads to low inference efficiency, because it usually takes 50 to 100 steps for diffusion to sample a token. This paper explores how to effectively address this issue. Our key motivation is that as more tokens are generated during the autoregressive process, subsequent tokens follow more constrained distributions and are easier to sample. To intuitively explain, if a model has generated part of a dog, the remaining tokens must complete the dog and thus are more constrained. Empirical evidence supports our motivation: at later generation stages, the next tokens can be well predicted by a multilayer perceptron, exhibit low variance, and follow closer-to-straight-line denoising paths from noise to tokens. Based on our finding, we introduce diffusion step annealing (DiSA), a training-free method which gradually uses fewer diffusion steps as more tokens are generated, e.g., using 50 steps at the beginning and gradually decreasing to 5 steps at later stages. Because DiSA is derived from our finding specific to diffusion in autoregressive models, it is complementary to existing acceleration methods designed for diffusion alone. DiSA can be implemented in only a few lines of code on existing models, and albeit simple, achieves 5-10times faster inference for MAR and Harmon and 1.4-2.5times for FlowAR and xAR, while maintaining the generation quality.

Diffusion models have opened the path to a wide range of text-based image editing frameworks. However, these typically build on the multi-step nature of the diffusion backwards process, and adapting them to distilled, fast-sampling methods has proven surprisingly challenging. Here, we focus on a popular line of text-based editing frameworks - the ``edit-friendly'' DDPM-noise inversion approach. We analyze its application to fast sampling methods and categorize its failures into two classes: the appearance of visual artifacts, and insufficient editing strength. We trace the artifacts to mismatched noise statistics between inverted noises and the expected noise schedule, and suggest a shifted noise schedule which corrects for this offset. To increase editing strength, we propose a pseudo-guidance approach that efficiently increases the magnitude of edits without introducing new artifacts. All in all, our method enables text-based image editing with as few as three diffusion steps, while providing novel insights into the mechanisms behind popular text-based editing approaches.

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.

Recent advances in generative AI have unveiled significant potential for the creation of 3D content. However, current methods either apply a pre-trained 2D diffusion model with the time-consuming score distillation sampling (SDS), or a direct 3D diffusion model trained on limited 3D data losing generation diversity. In this work, we approach the problem by employing a multi-view 2.5D diffusion fine-tuned from a pre-trained 2D diffusion model. The multi-view 2.5D diffusion directly models the structural distribution of 3D data, while still maintaining the strong generalization ability of the original 2D diffusion model, filling the gap between 2D diffusion-based and direct 3D diffusion-based methods for 3D content generation. During inference, multi-view normal maps are generated using the 2.5D diffusion, and a novel differentiable rasterization scheme is introduced to fuse the almost consistent multi-view normal maps into a consistent 3D model. We further design a normal-conditioned multi-view image generation module for fast appearance generation given the 3D geometry. Our method is a one-pass diffusion process and does not require any SDS optimization as post-processing. We demonstrate through extensive experiments that, our direct 2.5D generation with the specially-designed fusion scheme can achieve diverse, mode-seeking-free, and high-fidelity 3D content generation in only 10 seconds. Project page: https://nju-3dv.github.io/projects/direct25.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Recent 3D large reconstruction models typically employ a two-stage process, including first generate multi-view images by a multi-view diffusion model, and then utilize a feed-forward model to reconstruct images to 3D content.However, multi-view diffusion models often produce low-quality and inconsistent images, adversely affecting the quality of the final 3D reconstruction. To address this issue, we propose a unified 3D generation framework called Cycle3D, which cyclically utilizes a 2D diffusion-based generation module and a feed-forward 3D reconstruction module during the multi-step diffusion process. Concretely, 2D diffusion model is applied for generating high-quality texture, and the reconstruction model guarantees multi-view consistency.Moreover, 2D diffusion model can further control the generated content and inject reference-view information for unseen views, thereby enhancing the diversity and texture consistency of 3D generation during the denoising process. Extensive experiments demonstrate the superior ability of our method to create 3D content with high-quality and consistency compared with state-of-the-art baselines.

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.

The performance of single image super-resolution depends heavily on how to generate and complement high-frequency details to low-resolution images. Recently, diffusion-based models exhibit great potential in generating high-quality images for super-resolution tasks. However, existing models encounter difficulties in directly predicting high-frequency information of wide bandwidth by solely utilizing the high-resolution ground truth as the target for all sampling timesteps. To tackle this problem and achieve higher-quality super-resolution, we propose a novel Frequency Domain-guided multiscale Diffusion model (FDDiff), which decomposes the high-frequency information complementing process into finer-grained steps. In particular, a wavelet packet-based frequency complement chain is developed to provide multiscale intermediate targets with increasing bandwidth for reverse diffusion process. Then FDDiff guides reverse diffusion process to progressively complement the missing high-frequency details over timesteps. Moreover, we design a multiscale frequency refinement network to predict the required high-frequency components at multiple scales within one unified network. Comprehensive evaluations on popular benchmarks are conducted, and demonstrate that FDDiff outperforms prior generative methods with higher-fidelity super-resolution results.

Diffusion-based stylization methods typically denoise from a specific partial noise state for image-to-image and video-to-video tasks. This multi-step diffusion process is computationally expensive and hinders real-world application. A promising solution to speed up the process is to obtain few-step consistency models through trajectory distillation. However, current consistency models only force the initial-step alignment between the probability flow ODE (PF-ODE) trajectories of the student and the imperfect teacher models. This training strategy can not ensure the consistency of whole trajectories. To address this issue, we propose single trajectory distillation (STD) starting from a specific partial noise state. We introduce a trajectory bank to store the teacher model's trajectory states, mitigating the time cost during training. Besides, we use an asymmetric adversarial loss to enhance the style and quality of the generated images. Extensive experiments on image and video stylization demonstrate that our method surpasses existing acceleration models in terms of style similarity and aesthetic evaluations. Our code and results will be available on the project page: https://single-trajectory-distillation.github.io.

Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are increasingly replaced by data-driven deep generative models, and several groups have recently shown that state-of-the-art score-based diffusion models yield particularly strong performance and flexibility. In this paper, we show that the powerful paradigm of posterior sampling with diffusion models can be extended to include rich, structured, noise models. To that end, we propose a joint conditional reverse diffusion process with learned scores for the noise and signal-generating distribution. We demonstrate strong performance gains across various inverse problems with structured noise, outperforming competitive baselines that use normalizing flows and adversarial networks. This opens up new opportunities and relevant practical applications of diffusion modeling for inverse problems in the context of non-Gaussian measurement models.

We present an ultra-efficient post-training method for shortcutting large-scale pre-trained flow matching diffusion models into efficient few-step samplers, enabled by novel velocity field self-distillation. While shortcutting in flow matching, originally introduced by shortcut models, offers flexible trajectory-skipping capabilities, it requires a specialized step-size embedding incompatible with existing models unless retraining from scratchx2013a process nearly as costly as pretraining itself. Our key contribution is thus imparting a more aggressive shortcut mechanism to standard flow matching models (e.g., Flux), leveraging a unique distillation principle that obviates the need for step-size embedding. Working on the velocity field rather than sample space and learning rapidly from self-guided distillation in an online manner, our approach trains efficiently, e.g., producing a 3-step Flux less than one A100 day. Beyond distillation, our method can be incorporated into the pretraining stage itself, yielding models that inherently learn efficient, few-step flows without compromising quality. This capability also enables, to our knowledge, the first few-shot distillation method (e.g., 10 text-image pairs) for dozen-billion-parameter diffusion models, delivering state-of-the-art performance at almost free cost.

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.

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.

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.

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

Diffusion models achieve high-quality sample generation at the cost of a lengthy multistep inference procedure. To overcome this, diffusion distillation techniques produce student generators capable of matching or surpassing the teacher in a single step. However, the student model's inference speed is limited by the size of the teacher architecture, preventing real-time generation for computationally heavy applications. In this work, we introduce Multi-Student Distillation (MSD), a framework to distill a conditional teacher diffusion model into multiple single-step generators. Each student generator is responsible for a subset of the conditioning data, thereby obtaining higher generation quality for the same capacity. MSD trains multiple distilled students, allowing smaller sizes and, therefore, faster inference. Also, MSD offers a lightweight quality boost over single-student distillation with the same architecture. We demonstrate MSD is effective by training multiple same-sized or smaller students on single-step distillation using distribution matching and adversarial distillation techniques. With smaller students, MSD gets competitive results with faster inference for single-step generation. Using 4 same-sized students, MSD significantly outperforms single-student baseline counterparts and achieves remarkable FID scores for one-step image generation: 1.20 on ImageNet-64x64 and 8.20 on zero-shot COCO2014.

Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps to produce a sample. To accelerate sampling, we present denoising diffusion implicit models (DDIMs), a more efficient class of iterative implicit probabilistic models with the same training procedure as DDPMs. In DDPMs, the generative process is defined as the reverse of a Markovian diffusion process. We construct a class of non-Markovian diffusion processes that lead to the same training objective, but whose reverse process can be much faster to sample from. We empirically demonstrate that DDIMs can produce high quality samples 10 times to 50 times faster in terms of wall-clock time compared to DDPMs, allow us to trade off computation for sample quality, and can perform semantically meaningful image interpolation directly in the latent space.

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 16s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.

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.

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.

In this paper, we propose an efficient, fast, and versatile distillation method to accelerate the generation of pre-trained diffusion models: Flash Diffusion. The method reaches state-of-the-art performances in terms of FID and CLIP-Score for few steps image generation on the COCO2014 and COCO2017 datasets, while requiring only several GPU hours of training and fewer trainable parameters than existing methods. In addition to its efficiency, the versatility of the method is also exposed across several tasks such as text-to-image, inpainting, face-swapping, super-resolution and using different backbones such as UNet-based denoisers (SD1.5, SDXL) or DiT (Pixart-alpha), as well as adapters. In all cases, the method allowed to reduce drastically the number of sampling steps while maintaining very high-quality image generation. The official implementation is available at https://github.com/gojasper/flash-diffusion.

We introduce the Joint Video-Image Diffusion model (JVID), a novel approach to generating high-quality and temporally coherent videos. We achieve this by integrating two diffusion models: a Latent Image Diffusion Model (LIDM) trained on images and a Latent Video Diffusion Model (LVDM) trained on video data. Our method combines these models in the reverse diffusion process, where the LIDM enhances image quality and the LVDM ensures temporal consistency. This unique combination allows us to effectively handle the complex spatio-temporal dynamics in video generation. Our results demonstrate quantitative and qualitative improvements in producing realistic and coherent videos.

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.

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 relatively easy to train but require many steps to generate samples. Consistency models are far more difficult to train, but generate samples in a single step. In this paper we propose Multistep Consistency Models: A unification between Consistency Models (Song et al., 2023) and TRACT (Berthelot et al., 2023) that can interpolate between a consistency model and a diffusion model: a trade-off between sampling speed and sampling quality. Specifically, a 1-step consistency model is a conventional consistency model whereas we show that a infty-step consistency model is a diffusion model. Multistep Consistency Models work really well in practice. By increasing the sample budget from a single step to 2-8 steps, we can train models more easily that generate higher quality samples, while retaining much of the sampling speed benefits. Notable results are 1.4 FID on Imagenet 64 in 8 step and 2.1 FID on Imagenet128 in 8 steps with consistency distillation. We also show that our method scales to a text-to-image diffusion model, generating samples that are very close to the quality of the original model.

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.

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

Diffusion models achieve remarkable generation quality but suffer from computational intensive sampling due to suboptimal step discretization. While existing works focus on optimizing denoising directions, we address the principled design of stepsize schedules. This paper proposes Optimal Stepsize Distillation, a dynamic programming framework that extracts theoretically optimal schedules by distilling knowledge from reference trajectories. By reformulating stepsize optimization as recursive error minimization, our method guarantees global discretization bounds through optimal substructure exploitation. Crucially, the distilled schedules demonstrate strong robustness across architectures, ODE solvers, and noise schedules. Experiments show 10x accelerated text-to-image generation while preserving 99.4% performance on GenEval. Our code is available at https://github.com/bebebe666/OptimalSteps.

Diffusion models have recently shown great promise for generative modeling, outperforming GANs on perceptual quality and autoregressive models at density estimation. A remaining downside is their slow sampling time: generating high quality samples takes many hundreds or thousands of model evaluations. Here we make two contributions to help eliminate this downside: First, we present new parameterizations of diffusion models that provide increased stability when using few sampling steps. Second, we present a method to distill a trained deterministic diffusion sampler, using many steps, into a new diffusion model that takes half as many sampling steps. We then keep progressively applying this distillation procedure to our model, halving the number of required sampling steps each time. On standard image generation benchmarks like CIFAR-10, ImageNet, and LSUN, we start out with state-of-the-art samplers taking as many as 8192 steps, and are able to distill down to models taking as few as 4 steps without losing much perceptual quality; achieving, for example, a FID of 3.0 on CIFAR-10 in 4 steps. Finally, we show that the full progressive distillation procedure does not take more time than it takes to train the original model, thus representing an efficient solution for generative modeling using diffusion at both train and test time.

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.

The diffusion model is a state-of-the-art generative model that generates an image by applying a neural network iteratively. Moreover, this generation process is regarded as an algorithm solving an ordinary differential equation or a stochastic differential equation. Based on the analysis of the truncation error of the diffusion ODE and SDE, our study proposes a training-free algorithm that generates high-quality 512 x 512 and 1024 x 1024 images in eight steps, with flexible guidance scales. To the best of my knowledge, our algorithm is the first one that samples a 1024 x 1024 resolution image in 8 steps with an FID performance comparable to that of the latest distillation model, but without additional training. Meanwhile, our algorithm can also generate a 512 x 512 image in 8 steps, and its FID performance is better than the inference result using state-of-the-art ODE solver DPM++ 2m in 20 steps. We validate our eight-step image generation algorithm using the COCO 2014, COCO 2017, and LAION datasets. And our best FID performance is 15.7, 22.35, and 17.52. While the FID performance of DPM++2m is 17.3, 23.75, and 17.33. Further, it also outperforms the state-of-the-art AMED-plugin solver, whose FID performance is 19.07, 25.50, and 18.06. We also apply the algorithm in five-step inference without additional training, for which the best FID performance in the datasets mentioned above is 19.18, 23.24, and 19.61, respectively, and is comparable to the performance of the state-of-the-art AMED Pulgin solver in eight steps, SDXL-turbo in four steps, and the state-of-the-art diffusion distillation model Flash Diffusion in five steps. We also validate our algorithm in synthesizing 1024 * 1024 images within 6 steps, whose FID performance only has a limited distance to the latest distillation algorithm. The code is in repo: https://github.com/TheLovesOfLadyPurple/Hyperparameters-are-all-you-need

Denoising Diffusion Probabilistic Models (DDPMs) have garnered popularity for data generation across various domains. However, a significant bottleneck is the necessity for whole-network computation during every step of the generative process, leading to high computational overheads. This paper presents a novel framework, Denoising Diffusion Step-aware Models (DDSM), to address this challenge. Unlike conventional approaches, DDSM employs a spectrum of neural networks whose sizes are adapted according to the importance of each generative step, as determined through evolutionary search. This step-wise network variation effectively circumvents redundant computational efforts, particularly in less critical steps, thereby enhancing the efficiency of the diffusion model. Furthermore, the step-aware design can be seamlessly integrated with other efficiency-geared diffusion models such as DDIMs and latent diffusion, thus broadening the scope of computational savings. Empirical evaluations demonstrate that DDSM achieves computational savings of 49% for CIFAR-10, 61% for CelebA-HQ, 59% for LSUN-bedroom, 71% for AFHQ, and 76% for ImageNet, all without compromising the generation quality. Our code and models will be publicly available.

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 introduce NitroFusion, a fundamentally different approach to single-step diffusion that achieves high-quality generation through a dynamic adversarial framework. While one-step methods offer dramatic speed advantages, they typically suffer from quality degradation compared to their multi-step counterparts. Just as a panel of art critics provides comprehensive feedback by specializing in different aspects like composition, color, and technique, our approach maintains a large pool of specialized discriminator heads that collectively guide the generation process. Each discriminator group develops expertise in specific quality aspects at different noise levels, providing diverse feedback that enables high-fidelity one-step generation. Our framework combines: (i) a dynamic discriminator pool with specialized discriminator groups to improve generation quality, (ii) strategic refresh mechanisms to prevent discriminator overfitting, and (iii) global-local discriminator heads for multi-scale quality assessment, and unconditional/conditional training for balanced generation. Additionally, our framework uniquely supports flexible deployment through bottom-up refinement, allowing users to dynamically choose between 1-4 denoising steps with the same model for direct quality-speed trade-offs. Through comprehensive experiments, we demonstrate that NitroFusion significantly outperforms existing single-step methods across multiple evaluation metrics, particularly excelling in preserving fine details and global consistency.

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.

Denoising diffusion probabilistic models have recently received much research attention since they outperform alternative approaches, such as GANs, and currently provide state-of-the-art generative performance. The superior performance of diffusion models has made them an appealing tool in several applications, including inpainting, super-resolution, and semantic editing. In this paper, we demonstrate that diffusion models can also serve as an instrument for semantic segmentation, especially in the setup when labeled data is scarce. In particular, for several pretrained diffusion models, we investigate the intermediate activations from the networks that perform the Markov step of the reverse diffusion process. We show that these activations effectively capture the semantic information from an input image and appear to be excellent pixel-level representations for the segmentation problem. Based on these observations, we describe a simple segmentation method, which can work even if only a few training images are provided. Our approach significantly outperforms the existing alternatives on several datasets for the same amount of human supervision.

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.

We present a probabilistic model for point cloud generation, which is fundamental for various 3D vision tasks such as shape completion, upsampling, synthesis and data augmentation. Inspired by the diffusion process in non-equilibrium thermodynamics, we view points in point clouds as particles in a thermodynamic system in contact with a heat bath, which diffuse from the original distribution to a noise distribution. Point cloud generation thus amounts to learning the reverse diffusion process that transforms the noise distribution to the distribution of a desired shape. Specifically, we propose to model the reverse diffusion process for point clouds as a Markov chain conditioned on certain shape latent. We derive the variational bound in closed form for training and provide implementations of the model. Experimental results demonstrate that our model achieves competitive performance in point cloud generation and auto-encoding. The code is available at https://github.com/luost26/diffusion-point-cloud.

Head and neck (H&N) cancers are among the most prevalent types of cancer worldwide, and [18F]F-FDG PET/CT is widely used for H&N cancer management. Recently, the diffusion model has demonstrated remarkable performance in various image-generation tasks. In this work, we proposed a 3D diffusion model to accurately perform H&N tumor segmentation from 3D PET and CT volumes. The 3D diffusion model was developed considering the 3D nature of PET and CT images acquired. During the reverse process, the model utilized a 3D UNet structure and took the concatenation of PET, CT, and Gaussian noise volumes as the network input to generate the tumor mask. Experiments based on the HECKTOR challenge dataset were conducted to evaluate the effectiveness of the proposed diffusion model. Several state-of-the-art techniques based on U-Net and Transformer structures were adopted as the reference methods. Benefits of employing both PET and CT as the network input as well as further extending the diffusion model from 2D to 3D were investigated based on various quantitative metrics and the uncertainty maps generated. Results showed that the proposed 3D diffusion model could generate more accurate segmentation results compared with other methods. Compared to the diffusion model in 2D format, the proposed 3D model yielded superior results. Our experiments also highlighted the advantage of utilizing dual-modality PET and CT data over only single-modality data for H&N tumor segmentation.

In this paper, we present a novel diffusion model called that generates multiview-consistent images from a single-view image. Using pretrained large-scale 2D diffusion models, recent work Zero123 demonstrates the ability to generate plausible novel views from a single-view image of an object. However, maintaining consistency in geometry and colors for the generated images remains a challenge. To address this issue, we propose a synchronized multiview diffusion model that models the joint probability distribution of multiview images, enabling the generation of multiview-consistent images in a single reverse process. SyncDreamer synchronizes the intermediate states of all the generated images at every step of the reverse process through a 3D-aware feature attention mechanism that correlates the corresponding features across different views. Experiments show that SyncDreamer generates images with high consistency across different views, thus making it well-suited for various 3D generation tasks such as novel-view-synthesis, text-to-3D, and image-to-3D.

Recent advances in continuous generative models, including multi-step approaches like diffusion and flow-matching (typically requiring 8-1000 sampling steps) and few-step methods such as consistency models (typically 1-8 steps), have demonstrated impressive generative performance. However, existing work often treats these approaches as distinct paradigms, resulting in separate training and sampling methodologies. We introduce a unified framework for training, sampling, and analyzing these models. Our implementation, the Unified Continuous Generative Models Trainer and Sampler (UCGM-{T,S}), achieves state-of-the-art (SOTA) performance. For example, on ImageNet 256x256 using a 675M diffusion transformer, UCGM-T trains a multi-step model achieving 1.30 FID in 20 steps and a few-step model reaching 1.42 FID in just 2 steps. Additionally, applying UCGM-S to a pre-trained model (previously 1.26 FID at 250 steps) improves performance to 1.06 FID in only 40 steps. Code is available at: https://github.com/LINs-lab/UCGM.

Few-step diffusion or flow-based generative models typically distill a velocity-predicting teacher into a student that predicts a shortcut towards denoised data. This format mismatch has led to complex distillation procedures that often suffer from a quality-diversity trade-off. To address this, we propose policy-based flow models (pi-Flow). pi-Flow modifies the output layer of a student flow model to predict a network-free policy at one timestep. The policy then produces dynamic flow velocities at future substeps with negligible overhead, enabling fast and accurate ODE integration on these substeps without extra network evaluations. To match the policy's ODE trajectory to the teacher's, we introduce a novel imitation distillation approach, which matches the policy's velocity to the teacher's along the policy's trajectory using a standard ell_2 flow matching loss. By simply mimicking the teacher's behavior, pi-Flow enables stable and scalable training and avoids the quality-diversity trade-off. On ImageNet 256^2, it attains a 1-NFE FID of 2.85, outperforming MeanFlow of the same DiT architecture. On FLUX.1-12B and Qwen-Image-20B at 4 NFEs, pi-Flow achieves substantially better diversity than state-of-the-art few-step methods, while maintaining teacher-level quality.

In this research, we propose a novel denoising diffusion model based on shortest-path modeling that optimizes residual propagation to enhance both denoising efficiency and quality. Drawing on Denoising Diffusion Implicit Models (DDIM) and insights from graph theory, our model, termed the Shortest Path Diffusion Model (ShortDF), treats the denoising process as a shortest-path problem aimed at minimizing reconstruction error. By optimizing the initial residuals, we improve the efficiency of the reverse diffusion process and the quality of the generated samples. Extensive experiments on multiple standard benchmarks demonstrate that ShortDF significantly reduces diffusion time (or steps) while enhancing the visual fidelity of generated samples compared to prior arts. This work, we suppose, paves the way for interactive diffusion-based applications and establishes a foundation for rapid data generation. Code is available at https://github.com/UnicomAI/ShortDF.

Diffusion models (DMs) have significantly advanced the development of real-world image super-resolution (Real-ISR), but the computational cost of multi-step diffusion models limits their application. One-step diffusion models generate high-quality images in a one sampling step, greatly reducing computational overhead and inference latency. However, most existing one-step diffusion methods are constrained by the performance of the teacher model, where poor teacher performance results in image artifacts. To address this limitation, we propose FluxSR, a novel one-step diffusion Real-ISR technique based on flow matching models. We use the state-of-the-art diffusion model FLUX.1-dev as both the teacher model and the base model. First, we introduce Flow Trajectory Distillation (FTD) to distill a multi-step flow matching model into a one-step Real-ISR. Second, to improve image realism and address high-frequency artifact issues in generated images, we propose TV-LPIPS as a perceptual loss and introduce Attention Diversification Loss (ADL) as a regularization term to reduce token similarity in transformer, thereby eliminating high-frequency artifacts. Comprehensive experiments demonstrate that our method outperforms existing one-step diffusion-based Real-ISR methods. The code and model will be released at https://github.com/JianzeLi-114/FluxSR.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the reverse generation process, without modifying the original denoising diffusion process. However, since the degraded images already include low-frequency information, starting from Gaussian white noise will result in increased sampling steps. We propose Resfusion, a general framework that incorporates the residual term into the diffusion forward process, starting the reverse process directly from the noisy degraded images. The form of our inference process is consistent with the DDPM. We introduced a weighted residual noise, named resnoise, as the prediction target and explicitly provide the quantitative relationship between the residual term and the noise term in resnoise. By leveraging a smooth equivalence transformation, Resfusion determine the optimal acceleration step and maintains the integrity of existing noise schedules, unifying the training and inference processes. The experimental results demonstrate that Resfusion exhibits competitive performance on ISTD dataset, LOL dataset and Raindrop dataset with only five sampling steps. Furthermore, Resfusion can be easily applied to image generation and emerges with strong versatility. Our code and model are available at https://github.com/nkicsl/Resfusion.

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 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.

Despite significant advancements in customizing text-to-image and video generation models, generating images and videos that effectively integrate multiple personalized concepts remains a challenging task. To address this, we present TweedieMix, a novel method for composing customized diffusion models during the inference phase. By analyzing the properties of reverse diffusion sampling, our approach divides the sampling process into two stages. During the initial steps, we apply a multiple object-aware sampling technique to ensure the inclusion of the desired target objects. In the later steps, we blend the appearances of the custom concepts in the de-noised image space using Tweedie's formula. Our results demonstrate that TweedieMix can generate multiple personalized concepts with higher fidelity than existing methods. Moreover, our framework can be effortlessly extended to image-to-video diffusion models, enabling the generation of videos that feature multiple personalized concepts. Results and source code are in our anonymous project page.

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of DPMs is guided sampling, which usually needs a large guidance scale to obtain the best sample quality. The commonly-used fast sampler for guided sampling is DDIM, a first-order diffusion ODE solver that generally needs 100 to 250 steps for high-quality samples. Although recent works propose dedicated high-order solvers and achieve a further speedup for sampling without guidance, their effectiveness for guided sampling has not been well-tested before. In this work, we demonstrate that previous high-order fast samplers suffer from instability issues, and they even become slower than DDIM when the guidance scale grows large. To further speed up guided sampling, we propose DPM-Solver++, a high-order solver for the guided sampling of DPMs. DPM-Solver++ solves the diffusion ODE with the data prediction model and adopts thresholding methods to keep the solution matches training data distribution. We further propose a multistep variant of DPM-Solver++ to address the instability issue by reducing the effective step size. Experiments show that DPM-Solver++ can generate high-quality samples within only 15 to 20 steps for guided sampling by pixel-space and latent-space DPMs.

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.

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.

A diffusion model, which is formulated to produce an image using thousands of denoising steps, usually suffers from a slow inference speed. Existing acceleration algorithms simplify the sampling by skipping most steps yet exhibit considerable performance degradation. By viewing the generation of diffusion models as a discretized integrating process, we argue that the quality drop is partly caused by applying an inaccurate integral direction to a timestep interval. To rectify this issue, we propose a timestep aligner that helps find a more accurate integral direction for a particular interval at the minimum cost. Specifically, at each denoising step, we replace the original parameterization by conditioning the network on a new timestep, which is obtained by aligning the sampling distribution to the real distribution. Extensive experiments show that our plug-in design can be trained efficiently and boost the inference performance of various state-of-the-art acceleration methods, especially when there are few denoising steps. For example, when using 10 denoising steps on the popular LSUN Bedroom dataset, we improve the FID of DDIM from 9.65 to 6.07, simply by adopting our method for a more appropriate set of timesteps. Code will be made publicly available.

Latent Diffusion models (LDMs) have achieved remarkable results in synthesizing high-resolution images. However, the iterative sampling process is computationally intensive and leads to slow generation. Inspired by Consistency Models (song et al.), we propose Latent Consistency Models (LCMs), enabling swift inference with minimal steps on any pre-trained LDMs, including Stable Diffusion (rombach et al). Viewing the guided reverse diffusion process as solving an augmented probability flow ODE (PF-ODE), LCMs are designed to directly predict the solution of such ODE in latent space, mitigating the need for numerous iterations and allowing rapid, high-fidelity sampling. Efficiently distilled from pre-trained classifier-free guided diffusion models, a high-quality 768 x 768 2~4-step LCM takes only 32 A100 GPU hours for training. Furthermore, we introduce Latent Consistency Fine-tuning (LCF), a novel method that is tailored for fine-tuning LCMs on customized image datasets. Evaluation on the LAION-5B-Aesthetics dataset demonstrates that LCMs achieve state-of-the-art text-to-image generation performance with few-step inference. Project Page: https://latent-consistency-models.github.io/

Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis. However, their deployment faces challenges due to the high dimensionality of the state space, necessitating the development of efficient inference algorithms. Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as tau-leaping. While exact methods suffer from unpredictable inference time and redundant function evaluations, tau-leaping is limited by its first-order accuracy. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models, enabling larger step sizes while reducing error. We rigorously analyze the proposed schemes and establish the second-order accuracy of the theta-trapezoidal method in KL divergence. Empirical evaluations on GPT-2 level text and ImageNet-level image generation tasks demonstrate that our method achieves superior sample quality compared to existing approaches under equivalent computational constraints.

It is well known that many open-released foundational diffusion models have difficulty in generating images that substantially depart from average brightness, despite such images being present in the training data. This is due to an inconsistency: while denoising starts from pure Gaussian noise during inference, the training noise schedule retains residual data even in the final timestep distribution, due to difficulties in numerical conditioning in mainstream formulation, leading to unintended bias during inference. To mitigate this issue, certain epsilon-prediction models are combined with an ad-hoc offset-noise methodology. In parallel, some contemporary models have adopted zero-terminal SNR noise schedules together with v-prediction, which necessitate major alterations to pre-trained models. However, such changes risk destabilizing a large multitude of community-driven applications anchored on these pre-trained models. In light of this, our investigation revisits the fundamental causes, leading to our proposal of an innovative and principled remedy, called One More Step (OMS). By integrating a compact network and incorporating an additional simple yet effective step during inference, OMS elevates image fidelity and harmonizes the dichotomy between training and inference, while preserving original model parameters. Once trained, various pre-trained diffusion models with the same latent domain can share the same OMS module.

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.

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

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed solver schedule has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose S^3, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that S^3 can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply S^3 to Stable-Diffusion model and get an acceleration ratio of 2times, showing the feasibility of sampling in very few steps without retraining the neural network.

Recent approaches have yielded promising results in distilling multi-step text-to-image diffusion models into one-step ones. The state-of-the-art efficient distillation technique, i.e., SwiftBrushv2 (SBv2), even surpasses the teacher model's performance with limited resources. However, our study reveals its instability when handling different diffusion model backbones due to using a fixed guidance scale within the Variational Score Distillation (VSD) loss. Another weakness of the existing one-step diffusion models is the missing support for negative prompt guidance, which is crucial in practical image generation. This paper presents SNOOPI, a novel framework designed to address these limitations by enhancing the guidance in one-step diffusion models during both training and inference. First, we effectively enhance training stability through Proper Guidance-SwiftBrush (PG-SB), which employs a random-scale classifier-free guidance approach. By varying the guidance scale of both teacher models, we broaden their output distributions, resulting in a more robust VSD loss that enables SB to perform effectively across diverse backbones while maintaining competitive performance. Second, we propose a training-free method called Negative-Away Steer Attention (NASA), which integrates negative prompts into one-step diffusion models via cross-attention to suppress undesired elements in generated images. Our experimental results show that our proposed methods significantly improve baseline models across various metrics. Remarkably, we achieve an HPSv2 score of 31.08, setting a new state-of-the-art benchmark for one-step diffusion models.

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 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 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 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.

Flow-based 3D generation models typically require dozens of sampling steps during inference. Though few-step distillation methods, particularly Consistency Models (CMs), have achieved substantial advancements in accelerating 2D diffusion models, they remain under-explored for more complex 3D generation tasks. In this study, we propose a novel framework, MDT-dist, for few-step 3D flow distillation. Our approach is built upon a primary objective: distilling the pretrained model to learn the Marginal-Data Transport. Directly learning this objective needs to integrate the velocity fields, while this integral is intractable to be implemented. Therefore, we propose two optimizable objectives, Velocity Matching (VM) and Velocity Distillation (VD), to equivalently convert the optimization target from the transport level to the velocity and the distribution level respectively. Velocity Matching (VM) learns to stably match the velocity fields between the student and the teacher, but inevitably provides biased gradient estimates. Velocity Distillation (VD) further enhances the optimization process by leveraging the learned velocity fields to perform probability density distillation. When evaluated on the pioneer 3D generation framework TRELLIS, our method reduces sampling steps of each flow transformer from 25 to 1 or 2, achieving 0.68s (1 step x 2) and 0.94s (2 steps x 2) latency with 9.0x and 6.5x speedup on A800, while preserving high visual and geometric fidelity. Extensive experiments demonstrate that our method significantly outperforms existing CM distillation methods, and enables TRELLIS to achieve superior performance in few-step 3D generation.

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.

We introduce Score identity Distillation (SiD), an innovative data-free method that distills the generative capabilities of pretrained diffusion models into a single-step generator. SiD not only facilitates an exponentially fast reduction in Fr\'echet inception distance (FID) during distillation but also approaches or even exceeds the FID performance of the original teacher diffusion models. By reformulating forward diffusion processes as semi-implicit distributions, we leverage three score-related identities to create an innovative loss mechanism. This mechanism achieves rapid FID reduction by training the generator using its own synthesized images, eliminating the need for real data or reverse-diffusion-based generation, all accomplished within significantly shortened generation time. Upon evaluation across four benchmark datasets, the SiD algorithm demonstrates high iteration efficiency during distillation and surpasses competing distillation approaches, whether they are one-step or few-step, data-free, or dependent on training data, in terms of generation quality. This achievement not only redefines the benchmarks for efficiency and effectiveness in diffusion distillation but also in the broader field of diffusion-based generation. The PyTorch implementation is available at https://github.com/mingyuanzhou/SiD

In this paper, we unify more than 10 existing one-step diffusion distillation approaches, such as Diff-Instruct, DMD, SIM, SiD, f-distill, etc, inside a theory-driven framework which we name the \emph{Uni-Instruct}. Uni-Instruct is motivated by our proposed diffusion expansion theory of the f-divergence family. Then we introduce key theories that overcome the intractability issue of the original expanded f-divergence, resulting in an equivalent yet tractable loss that effectively trains one-step diffusion models by minimizing the expanded f-divergence family. The novel unification introduced by Uni-Instruct not only offers new theoretical contributions that help understand existing approaches from a high-level perspective but also leads to state-of-the-art one-step diffusion generation performances. On the CIFAR10 generation benchmark, Uni-Instruct achieves record-breaking Frechet Inception Distance (FID) values of \emph{1.46} for unconditional generation and \emph{1.38} for conditional generation. On the ImageNet-64times 64 generation benchmark, Uni-Instruct achieves a new SoTA one-step generation FID of \emph{1.02}, which outperforms its 79-step teacher diffusion with a significant improvement margin of 1.33 (1.02 vs 2.35). We also apply Uni-Instruct on broader tasks like text-to-3D generation. For text-to-3D generation, Uni-Instruct gives decent results, which slightly outperforms previous methods, such as SDS and VSD, in terms of both generation quality and diversity. Both the solid theoretical and empirical contributions of Uni-Instruct will potentially help future studies on one-step diffusion distillation and knowledge transferring of diffusion models.

Text-to-image diffusion models can create stunning images from natural language descriptions that rival the work of professional artists and photographers. However, these models are large, with complex network architectures and tens of denoising iterations, making them computationally expensive and slow to run. As a result, high-end GPUs and cloud-based inference are required to run diffusion models at scale. This is costly and has privacy implications, especially when user data is sent to a third party. To overcome these challenges, we present a generic approach that, for the first time, unlocks running text-to-image diffusion models on mobile devices in less than 2 seconds. We achieve so by introducing efficient network architecture and improving step distillation. Specifically, we propose an efficient UNet by identifying the redundancy of the original model and reducing the computation of the image decoder via data distillation. Further, we enhance the step distillation by exploring training strategies and introducing regularization from classifier-free guidance. Our extensive experiments on MS-COCO show that our model with 8 denoising steps achieves better FID and CLIP scores than Stable Diffusion v1.5 with 50 steps. Our work democratizes content creation by bringing powerful text-to-image diffusion models to the hands of users.

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.

Multistep instructions, such as recipes and how-to guides, greatly benefit from visual aids, such as a series of images that accompany the instruction steps. While Large Language Models (LLMs) have become adept at generating coherent textual steps, Large Vision/Language Models (LVLMs) are less capable of generating accompanying image sequences. The most challenging aspect is that each generated image needs to adhere to the relevant textual step instruction, as well as be visually consistent with earlier images in the sequence. To address this problem, we propose an approach for generating consistent image sequences, which integrates a Latent Diffusion Model (LDM) with an LLM to transform the sequence into a caption to maintain the semantic coherence of the sequence. In addition, to maintain the visual coherence of the image sequence, we introduce a copy mechanism to initialise reverse diffusion processes with a latent vector iteration from a previously generated image from a relevant step. Both strategies will condition the reverse diffusion process on the sequence of instruction steps and tie the contents of the current image to previous instruction steps and corresponding images. Experiments show that the proposed approach is preferred by humans in 46.6% of the cases against 26.6% for the second best method. In addition, automatic metrics showed that the proposed method maintains semantic coherence and visual consistency across steps in both domains.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step t and corresponding state x_t, there might exist another time step t_s which exhibits superior coupling with x_t. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49\% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at https://github.com/Mingxiao-Li/TS-DPM.

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 model distillation has emerged as a powerful technique for creating efficient few-step and single-step generators. Among these, Distribution Matching Distillation (DMD) and its variants stand out for their impressive performance, which is widely attributed to their core mechanism of matching the student's output distribution to that of a pre-trained teacher model. In this work, we challenge this conventional understanding. Through a rigorous decomposition of the DMD training objective, we reveal that in complex tasks like text-to-image generation, where CFG is typically required for desirable few-step performance, the primary driver of few-step distillation is not distribution matching, but a previously overlooked component we identify as CFG Augmentation (CA). We demonstrate that this term acts as the core ``engine'' of distillation, while the Distribution Matching (DM) term functions as a ``regularizer'' that ensures training stability and mitigates artifacts. We further validate this decoupling by demonstrating that while the DM term is a highly effective regularizer, it is not unique; simpler non-parametric constraints or GAN-based objectives can serve the same stabilizing function, albeit with different trade-offs. This decoupling of labor motivates a more principled analysis of the properties of both terms, leading to a more systematic and in-depth understanding. This new understanding further enables us to propose principled modifications to the distillation process, such as decoupling the noise schedules for the engine and the regularizer, leading to further performance gains. Notably, our method has been adopted by the Z-Image ( https://github.com/Tongyi-MAI/Z-Image ) project to develop a top-tier 8-step image generation model, empirically validating the generalization and robustness of our findings.

In this work, we build upon our previous publication and use diffusion-based generative models for speech enhancement. We present a detailed overview of the diffusion process that is based on a stochastic differential equation and delve into an extensive theoretical examination of its implications. Opposed to usual conditional generation tasks, we do not start the reverse process from pure Gaussian noise but from a mixture of noisy speech and Gaussian noise. This matches our forward process which moves from clean speech to noisy speech by including a drift term. We show that this procedure enables using only 30 diffusion steps to generate high-quality clean speech estimates. By adapting the network architecture, we are able to significantly improve the speech enhancement performance, indicating that the network, rather than the formalism, was the main limitation of our original approach. In an extensive cross-dataset evaluation, we show that the improved method can compete with recent discriminative models and achieves better generalization when evaluating on a different corpus than used for training. We complement the results with an instrumental evaluation using real-world noisy recordings and a listening experiment, in which our proposed method is rated best. Examining different sampler configurations for solving the reverse process allows us to balance the performance and computational speed of the proposed method. Moreover, we show that the proposed method is also suitable for dereverberation and thus not limited to additive background noise removal. Code and audio examples are available online, see https://github.com/sp-uhh/sgmse

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on image quality. We enforce the one-step image generator match the diffusion model at distribution level, by minimizing an approximate KL divergence whose gradient can be expressed as the difference between 2 score functions, one of the target distribution and the other of the synthetic distribution being produced by our one-step generator. The score functions are parameterized as two diffusion models trained separately on each distribution. Combined with a simple regression loss matching the large-scale structure of the multi-step diffusion outputs, our method outperforms all published few-step diffusion approaches, reaching 2.62 FID on ImageNet 64x64 and 11.49 FID on zero-shot COCO-30k, comparable to Stable Diffusion but orders of magnitude faster. Utilizing FP16 inference, our model generates images at 20 FPS on modern hardware.

Diffusion models (DMs) excel in image generation, but suffer from slow inference and the training-inference discrepancies. Although gradient-based solvers like DPM-Solver accelerate the denoising inference, they lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers a reference-free way to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called EVODiff, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to 45.5\% (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by 25\% (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts. Code is available at https://github.com/ShiguiLi/EVODiff.

Diffusion models generate highly realistic images through learning a multi-step denoising process, naturally embodying the principles of multi-task learning (MTL). Despite the inherent connection between diffusion models and MTL, there remains an unexplored area in designing neural architectures that explicitly incorporate MTL into the framework of diffusion models. In this paper, we present Denoising Task Routing (DTR), a simple add-on strategy for existing diffusion model architectures to establish distinct information pathways for individual tasks within a single architecture by selectively activating subsets of channels in the model. What makes DTR particularly compelling is its seamless integration of prior knowledge of denoising tasks into the framework: (1) Task Affinity: DTR activates similar channels for tasks at adjacent timesteps and shifts activated channels as sliding windows through timesteps, capitalizing on the inherent strong affinity between tasks at adjacent timesteps. (2) Task Weights: During the early stages (higher timesteps) of the denoising process, DTR assigns a greater number of task-specific channels, leveraging the insight that diffusion models prioritize reconstructing global structure and perceptually rich contents in earlier stages, and focus on simple noise removal in later stages. Our experiments demonstrate that DTR consistently enhances the performance of diffusion models across various evaluation protocols, all without introducing additional parameters. Furthermore, DTR contributes to accelerating convergence during training. Finally, we show the complementarity between our architectural approach and existing MTL optimization techniques, providing a more complete view of MTL within the context of diffusion training.

Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants, lacking a unified analytical perspective. Besides, they indiscriminately reconstruct images through global noise injection and removal, inevitably distorting undegraded regions due to imperfect reconstruction. To address these challenges, we propose the Residual Diffusion Bridge Model (RDBM). Specifically, we theoretically reformulate the stochastic differential equations of generalized diffusion bridge and derive the analytical formulas of its forward and reverse processes. Crucially, we leverage the residuals from given distributions to modulate the noise injection and removal, enabling adaptive restoration of degraded regions while preserving intact others. Moreover, we unravel the fundamental mathematical essence of existing bridge models, all of which are special cases of RDBM and empirically demonstrate the optimality of our proposed models. Extensive experiments are conducted to demonstrate the state-of-the-art performance of our method both qualitatively and quantitatively across diverse image restoration tasks. Code is publicly available at https://github.com/MiliLab/RDBM.

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.