Exact Global MCMC with Denoising Diffusion

Abstract:This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional target densities. The method is motivated by the observation that sequentially applying a forward and reverse diffusion process defines a Markov chain with a target stationary distribution for an ideal denoiser trained on samples of the target distribution. This observation can be made exact for any denoiser by applying a Metropolis-Hastings step whose acceptance ratio includes the density of the forward and reverse paths of a discrete time SDE approximation. We therefore propose to train denoising diffusion models on locally convergent MALA samples to learn global MCMC proposals. We call the composition of the global denoiser-based path sampler and a local MALA sampler Denoising Diffusion Monte Carlo (DDMC). Experiments show that DDMC can provide global proposals with high acceptance across a variety of complex target densities. Our results offer preliminary evidence that the established scaling behavior of standard diffusion training transfers directly to exact sampling from high-dimensional unnormalized densities.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.00279 [stat.ML]

(or arXiv:2609.00279v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.00279 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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