Evaluating diffusion-based methods for Bayesian inverse problems
Ludovic Laszlo Reymond, Intern at EPFL

Seminar • 2024-11-26

Abstract
Diffusion models have emerged as a powerful method for learning highly complex distributions. As a result, many attempts have been made to use diffusion models as priors for solving inverse problems. However, most of these diffusion-based solvers have no theoretical guarantees and often fail to capture the posterior distribution. We evaluate one such method on synthetic datasets consisting of sparse stochastic processes (SSPs), where the true posterior distribution is known for any given linear measurement operator. In particular, we have access to the MMSE denoiser, which we show can replace the neural network component of the diffusion-based solver. We find that this does not improve its performance, revealing that there are intrinsic problems in the design of the method due to approximations and heuristic choices.