From denoising diffusions to denoising Markov models

• 成果类型: Article
• 署名作者: Benton, Joe; Shi, Yuyang; De Bortoli, Valentin; Deligiannidis, George; Doucet, Arnaud
• 署名单位: University of Oxford; Universite PSL; Ecole Normale Superieure (ENS)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae005
• 发表日期: 2024
• 关键词: approximate bayesian computation

摘要

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain synthetic datapoints. The denoising diffusion relies on approximations of the logarithmic derivatives of the noised data densities using score matching. Such models can also be used to perform approximate posterior simulation when one can only sample from the prior and likelihood. We propose a unifying framework generalizing this approach to a wide class of spaces and leading to an original extension of score matching. We illustrate the resulting models on various applications.