Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spaces

TL;DR

This paper introduces off-policy training methods for discrete diffusion samplers, enhancing their efficiency and extending their application to bridging distributions and data-free posterior sampling in discrete latent spaces.

Contribution

It presents novel off-policy training techniques for discrete diffusion samplers and generalizes them to distribution bridging and data-free posterior sampling.

Findings

Improved performance of discrete samplers on benchmarks

Successful application to data-free posterior sampling in image models

Extension of diffusion methods to discrete latent spaces

Abstract

Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and efficient sampling from an unnormalised density. Such algorithms have been widely studied for continuous-space sampling tasks; however, their application to problems in discrete space remains largely unexplored. Although some progress has been made in this area, discrete diffusion samplers do not take full advantage of ideas commonly used for continuous-space sampling. In this paper, we propose to bridge this gap by introducing off-policy training techniques for discrete diffusion samplers. We show that these techniques improve the performance of discrete samplers on both established and new synthetic benchmarks. Next, we generalise discrete diffusion samplers to the task of bridging between two arbitrary distributions, introducing data-to-energy Schr\"odinger bridge training for the discrete domain for the first time. Lastly, we showcase the application of the proposed diffusion samplers to data-free posterior sampling in the discrete latent spaces of image generative models.