Diffusion Waltz: MCMC Posterior Sampling with Diffusion Priors in Three Steps

Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, and possibly non-differentiable, forward models remains challenging. We introduce _diffusion waltz_, an MCMC method that uses SDEdit-style noising–denoising as a proposal, corrected via Metropolis–Hastings to sample exactly from the posterior. We show that this sampling mechanism strictly generalizes preconditioned Crank–Nicolson (pCN) to learned prior settings, and, like pCN, can sample from the posterior without ever evaluating the prior density. To improve mixing, we further introduce _conditional noising_, which injects observation information directly into the proposal while preserving exactness. Across a range of nonlinear inverse problems, with or without access to gradients, diffusion waltz matches or outperforms existing baselines in reconstruction accuracy and uncertainty calibration.