Abstract Summary
•
The paper introduces SGDD, a discrete diffusion posterior sampling algorithm based on split Gibbs sampling, for solving inverse problems in discrete-state spaces.
•
SGDD demonstrates convergence to the target posterior distribution and outperforms existing baselines by more than 30% on benchmarks for discrete data like DNA sequence design and music infilling.
Abstract
We study the problem of posterior sampling in discrete-state spaces using discrete diffusion models. While posterior sampling methods for continuous diffusion models have achieved remarkable progress, analogous methods for discrete diffusion models remain challenging. In this work, we introduce a principled plug-and-play discrete diffusion posterior sampling algorithm based on split Gibbs sampling, which we call SGDD. Our algorithm enables reward-guided generation and solving inverse problems in discrete-state spaces. We demonstrate the convergence of SGDD to the target posterior distribution and verify this through controlled experiments on synthetic benchmarks. Our method enjoys state-of-the-art posterior sampling performance on a range of benchmarks for discrete data, including DNA sequence design, discrete image inverse problems, and music infilling, achieving more than 30% improved performance compared to existing baselines.