Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
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.
| Authors | So Takao, Gregory David Bellchambers, Luke Ye et al. |
|---|---|
| Primary category | cs.LG |
| Published | 7 October 2026 |
| Last updated at source | 7 October 2026 |
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