Particle Denoising Diffusion Sampler

TL;DR

The paper introduces Particle Denoising Diffusion Sampler (PDDS), a novel method for sampling from unnormalized densities using an iterative particle scheme with score matching, achieving asymptotic consistency.

Contribution

It presents a new particle-based diffusion sampling method that is asymptotically consistent, differing from standard diffusion models by handling unnormalized densities.

Findings

Demonstrates effectiveness on multimodal sampling tasks

Achieves asymptotic consistency under mild assumptions

Applicable to high-dimensional problems

Abstract

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by estimating the time-reversal of this diffusion using score matching ideas. We follow here a similar strategy to sample from unnormalized probability densities and compute their normalizing constants. However, the time-reversed diffusion is here simulated by using an original iterative particle scheme relying on a novel score matching loss. Contrary to standard denoising diffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS) provides asymptotically consistent estimates under mild assumptions. We demonstrate PDDS on multimodal and high dimensional sampling tasks.