MRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE Solvers

• URL: http://arxiv.org/abs/2502.07856v3
• Date: Wed, 19 Feb 2025 05:22:54 GMT
• Title: MRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE Solvers
• Authors: Ao Li, Wei Fang, Hongbo Zhao, Le Lu, Ge Yang, Minfeng Xu,
• Abstract summary: Mean Reverting (MR) Diffusion directly modifies the structure of the differential equation (SDE) Current training-free fast samplers are not directly applicable to MR Diffusion. We propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion.
• Score: 12.639167101005695
• License:
• Abstract: 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.

Related papers

• An Ordinary Differential Equation Sampler with Stochastic Start for Diffusion Bridge Models [13.00429687431982]
  Diffusion bridge models initialize the generative process from corrupted images instead of pure Gaussian noise. Existing diffusion bridge models often rely on Differential Equation samplers, which result in slower inference speed. We propose a high-order ODE sampler with a start for diffusion bridge models. Our method is fully compatible with pretrained diffusion bridge models and requires no additional training.
  arXiv  Detail & Related papers  (2024-12-28T03:32:26Z)
• Diffusion Rejection Sampling [13.945372555871414]
  Diffusion Rejection Sampling (DiffRS) is a rejection sampling scheme that aligns the sampling transition kernels with the true ones at each timestep. The proposed method can be viewed as a mechanism that evaluates the quality of samples at each intermediate timestep and refines them with varying effort depending on the sample. Empirical results demonstrate the state-of-the-art performance of DiffRS on the benchmark datasets and the effectiveness of DiffRS for fast diffusion samplers and large-scale text-to-image diffusion models.
  arXiv  Detail & Related papers  (2024-05-28T07:00:28Z)
• Gaussian Mixture Solvers for Diffusion Models [84.83349474361204]
  We introduce a novel class of SDE-based solvers called GMS for diffusion models. Our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis.
  arXiv  Detail & Related papers  (2023-11-02T02:05:38Z)
• SMRD: SURE-based Robust MRI Reconstruction with Diffusion Models [76.43625653814911]
  Diffusion models have gained popularity for accelerated MRI reconstruction due to their high sample quality. They can effectively serve as rich data priors while incorporating the forward model flexibly at inference time. We introduce SURE-based MRI Reconstruction with Diffusion models (SMRD) to enhance robustness during testing.
  arXiv  Detail & Related papers  (2023-10-03T05:05:35Z)
• Fast Diffusion Model [122.36693015093041]
  Diffusion models (DMs) have been adopted across diverse fields with their abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a DM optimization perspective.
  arXiv  Detail & Related papers  (2023-06-12T09:38:04Z)
• Solving Diffusion ODEs with Optimal Boundary Conditions for Better Image Super-Resolution [82.50210340928173]
  randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. We propose a plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. 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.
  arXiv  Detail & Related papers  (2023-05-24T17:09:54Z)
• Fast Sampling of Diffusion Models via Operator Learning [74.37531458470086]
  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 a parallel decoding method. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.
  arXiv  Detail & Related papers  (2022-11-24T07:30:27Z)
• DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps [45.612477740555406]
  Diffusion probabilistic models (DPMs) are emerging powerful generative models. DPM-r is suitable for both discrete-time and continuous-time DPMs without any further training. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset.
  arXiv  Detail & Related papers  (2022-06-02T08:43:16Z)
• Pseudo Numerical Methods for Diffusion Models on Manifolds [77.40343577960712]
  Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. DDPMs require hundreds to thousands of iterations to produce final samples. We propose pseudo numerical methods for diffusion models (PNDMs) PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup)
  arXiv  Detail & Related papers  (2022-02-20T10:37:52Z)
• Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction [31.61199061999173]
  Diffusion models have a critical downside - they are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. We show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. New sampling strategy, dubbed ComeCloser-DiffuseFaster (CCDF), also reveals a new insight on how the existing feedforward neural network approaches for inverse problems can be synergistically combined with the diffusion models.
  arXiv  Detail & Related papers  (2021-12-09T04:28:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.