Abstract
Diffusion models can be used to synthesize samples with complex distributions and have many 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 exploit 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, in order to guide simulations towards 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 impractical due to intractable terms, we propose an approach based on Gibbs sampling. We validate our approach with extensive experiments on inverse imaging problems. We use both pixel-space and latent-space diffusion priors, and consider source separation problems with an audio diffusion model.
