Plug & Play Diffusion models for general imaging inverse problems

Inverse problems arise across scientific imaging and signal processing, where the goal is to recover an unknown signal from indirect and often noisy observations. A principled approach is Bayesian inference, which characterizes uncertainty by sampling from the posterior distribution. However, the high dimensionality of modern problems and the complexity of realistic priors make posterior sampling challenging. Advances in generative modeling, particularly diffusion models, provide a promising route by enabling powerful learned priors through score functions. This talk introduces diffusion-based approaches for sampling posteriors in inverse problems, with a focus on plug-and-play diffusion methods. Diffusion models can estimate the score of the data prior, however the score of the likelihood term is typically intractable for many realistic forward models, requiring practical approximations within posterior sampling algorithms. Analytically approximating this likelihood term enables efficient posterior sampling that doesn’t require any retraining when the parameters of the forward problems changes> Although these methods show some desirable behaviour, such as their modularity and strong empirical performance, we will also discussed their limitations including potential bias from likelihood approximations, stability of the sampling dynamics, and scalability to complex or nonlinear inverse problems.