  This paper explores the use of score-based diffusion models for Bayesian
image reconstruction. Diffusion models are an efficient tool for generative
modeling. Diffusion models can also be used for solving image reconstruction
problems. We present a simple and flexible algorithm for training a diffusion
model and using it for maximum a posteriori reconstruction, minimum mean square
error reconstruction, and posterior sampling. We present experiments on both a
linear and a nonlinear reconstruction problem that highlight the strengths and
limitations of the approach.
