MRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE
  Solvers
Authors: name: Ao Li, name: Wei Fang, name: Hongbo Zhao, name: Le Lu, name: Ge Yang, name: Minfeng Xu

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.