Noise, Denoise, Correct：三步实现扩散先验的 MCMC 后验采样

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

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研究人员提出 diffusion waltz，一种用 SDEdit 式加噪-去噪作为提议、经 Metropolis-Hastings 校正的 MCMC 方法，可在不评估先验的情况下实现精确后验采样。该方法进一步通过无梯度的集合卡尔曼更新将观测注入提议并保持精确性，在不可微的 Navier-Stokes 初始条件恢复任务上，于不同噪声与非线性区间均优于现有基线。

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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.

Subjects:	Machine Learning (cs.LG)
Cite as:	arXiv:2610.09407 [cs.LG]
	(or arXiv:2610.09407v1 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2610.09407 arXiv-issued DOI via DataCite (pending registration)

Submission history

From: So Takao [view email]
[v1] Wed, 7 Oct 2026 04:06:19 UTC (1,076 KB)

来源：arXiv：cs.LG · arxiv.org