  Diffusion models (DMs) have recently shown outstanding capability in modeling
complex image distributions, making them expressive image priors for solving
Bayesian inverse problems. However, most existing DM-based methods rely on
approximations in the generative process to be generic to different inverse
problems, leading to inaccurate sample distributions that deviate from the
target posterior defined within the Bayesian framework. To harness the
generative power of DMs while avoiding such approximations, we propose a Markov
chain Monte Carlo algorithm that performs posterior sampling for general
inverse problems by reducing it to sampling the posterior of a Gaussian
denoising problem. Crucially, we leverage a general DM formulation as a unified
interface that allows for rigorously solving the denoising problem with a range
of state-of-the-art DMs. We demonstrate the effectiveness of the proposed
method on six inverse problems (three linear and three nonlinear), including a
real-world black hole imaging problem. Experimental results indicate that our
proposed method offers more accurate reconstructions and posterior estimation
compared to existing DM-based imaging inverse methods.
