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This paper presents "Diffusion Waltz," a novel MCMC framework that leverages pretrained diffusion models as priors to solve inverse problems involving nonlinear, non-differentiable forward models. By combining SDEdit-style noising-denoising proposals with Metropolis-Hastings corrections and gradient-free ensemble Kalman updates, the method achieves exact posterior sampling without requiring prior evaluation, demonstrating superior performance on Navier-Stokes recovery tasks.
Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
arXiv:2610.09407v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG)
arXiv:2610.09407 [cs.LG]
(or arXiv:2610.09407v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.09407 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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