REVERSE DIFFUSION MONTE CARLO

Xunpeng Huang, Hanze Dong, Yifan Hao, Yi An Ma, Tong Zhang

Research output: Contribution to conferencePaperpeer-review

Abstract

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.

Original languageEnglish (US)
StatePublished - 2024
Event12th International Conference on Learning Representations, ICLR 2024 - Hybrid, Vienna, Austria
Duration: May 7 2024May 11 2024

Conference

Conference12th International Conference on Learning Representations, ICLR 2024
Country/TerritoryAustria
CityHybrid, Vienna
Period5/7/245/11/24

ASJC Scopus subject areas

  • Language and Linguistics
  • Computer Science Applications
  • Education
  • Linguistics and Language

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