Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
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.
ProofPaper ↗
Key points
- Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard.
- 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.
Sources (1)
- [1]Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three StepsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 04:06 AM
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.
Pretrained diffusion models are powerful priors for inverse problems, but posterior sampling under nonlinear, non-differentiable forward models remain hard.
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