Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps

So Takao, Gregory David Bellchambers, Luke Ye, Sanmitra Ghosh, Michalis Michaelides

Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard. We introduce diffusion waltz, an MCMC method using SDEdit-style noising-denoising as a proposal, corrected via Metropolis-Hastings for exact posterior sampling without prior evaluation. We further propose injecting observations into the proposal while preserving exactness, using a gradient-free ensemble Kalman update. On a non-differentiable Navier-Stokes initial condition recovery task, diffusion waltz outperforms existing baselines across different noise and nonlinearity regimes.