Toward Principled Inference and Convergence Guarantees in Diffusion Models

“Toward Principled Inference and Convergence Guarantees in Diffusion Models”

SPEAKER: Alain Durmus (Ecole Polytechnique)

ABSTRACT:

The talk will be based on three contributions on diffusion models and their application to Bayesian inference. 

The first part of the talk will be on the use of diffusion models for solving inverse problems, such as image reconstruction or source separation. Here, I introduce a novel mixture-based posterior sampling framework that combines diffusion priors with observational data using a principled Gibbs sampling scheme. This approach offers theoretical guarantees, task-agnostic applicability, and robust performance across a wide range of problems—including ten image restoration tasks and musical source separation—without relying on crude approximations or heavy heuristic tuning.    

In the second part, I will shift to discrete diffusion models. First, I will revisit uniform discrete diffusion models, showing that the usual plug-in and marginalization parameterizations of the reverse transitions do not coincide. In particular, I will show that the plug-in parameterization is not optimized by the denoising posterior but by a leave-one-out posterior that removes the influence of the local observation.  As a by-product, it yields a Gibbs-based predictor–corrector scheme at no additional training cost. I will conclude this talk by presenting KL and TV convergence guarantees under minimal assumptions for a binary discrete score-based diffusion model.