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

arXiv: https://arxiv.org/abs/2610.09407 · HTML: https://mlsanity.com/paper/2610.09407/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- First posted on arXiv 7 Oct 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Abstract (arXiv)

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.