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

TL;DR

MaRS is a novel, training-free sampling algorithm that significantly accelerates mean reversion diffusion models, reducing the number of function evaluations needed for high-quality image generation by 10 to 20 times.

Contribution

The paper introduces MaRS, a semi-analytical, fast sampler for MR Diffusion that works across various parameterizations without training, improving sampling efficiency.

Findings

Achieves 10-20x speedup in sampling

Maintains high quality across multiple tasks

Supports all mainstream parameterizations

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 MaRS (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.