Abstract
Diffusion models allow for the synthesis of samples from complex distributions and have numerous applications in data generation. Recently, they have been used as priors for solving Bayesian inverse problems.
This presentation provides an overview of current methods that leverage pre-trained diffusion models in conjunction with Monte Carlo methods to solve Bayesian inverse problems without requiring additional training. We show that these methods rely primarily on modifying the intermediate distributions of the diffusion process to guide the simulations toward the posterior distribution. We then describe how different Monte Carlo methods are used to facilitate sampling from these modified distributions.
We also present a new method based on a mixture approximation of the modified intermediate distributions. Since direct gradient-based sampling of these mixtures is infeasible due to intractable terms, we propose an approach based on Gibbs sampling. We validate our approach through extensive experiments on inverse imaging problems. We use diffusion priors in both pixel space and latent space, and consider source separation problems with an audio diffusion model.
