title: MRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE
    Solvers
summary: 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.
paper_authors._id: 67b2dedc8a276e7b485a9bcd
paper_authors.name: Ao Li
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-03-12T20:46:19.025Z
paper_authors._id: 64fe6f5958718aaa93264e62
paper_authors.avatarUrl: /avatars/75688072f466723dd5f5dba8cdd7536a.svg
paper_authors.fullname: Ao Li
paper_authors.type: user
paper_authors.user: 321rf13
paper_authors._id: 67b2dedc8a276e7b485a9bce
paper_authors.name: Wei Fang
paper_authors._id: 67b2dedc8a276e7b485a9bcf
paper_authors.name: Hongbo Zhao
paper_authors.status: claimed_verified
paper_authors.statusLastChangedAt: 2025-02-18T09:32:42.698Z
paper_authors._id: 64100834c025ddf6189c415e
paper_authors.avatarUrl: /avatars/9b9bbecef5d5815540abf92d74012f55.svg
paper_authors.fullname: Hongbo Zhao
paper_authors.type: user
paper_authors.user: z-hb
paper_authors._id: 67b2dedc8a276e7b485a9bd0
paper_authors.name: Le Lu
paper_authors._id: 67b2dedc8a276e7b485a9bd1
paper_authors.name: Ge Yang
paper_authors._id: 67b2dedc8a276e7b485a9bd2
paper_authors.name: Minfeng Xu
paper_title: MRS: A Fast Sampler for Mean Reverting Diffusion based on ODE and SDE
    Solvers
paper_summary: 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.
paper_ai_summary: A new algorithm, MR Sampler, reduces the sampling steps and enhances the speed of Mean Reverting Diffusion while maintaining high quality across image restoration tasks.
paper_ai_keywords: diffusion models controllable generation score function Mean Reverting (MR) Diffusion stochastic differential equation (SDE) image conditions sampling NFEs (number of function evaluations) reverse-time SDE probability flow ordinary differential equation (PF-ODE) semi-analytical solutions neural network noise prediction data prediction velocity prediction image restoration tasks