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arXiv Machine Learning

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

The paper introduces Diffusion Waltz, an MCMC algorithm that uses SDEdit-style noising and denoising as a proposal and corrects it with Metropolis-Hastings to achieve exact posterior sampling without evaluating the prior. It also incorporates observations into the proposal via a gradient‑free ensemble Kalman update while maintaining exactness. In experiments on a non‑differentiable Navier‑Stokes initial‑condition recovery problem, Diffusion Waltz outperforms existing baselines across various noise and nonlinearity regimes.

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arXiv Statistics ML
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Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding

The paper introduces a learning-based approach to replace the MCMC step in split-Gibbs diffusion posterior sampling. By reformulating both Gibbs updates as Gaussian denoising problems, the method uses ODE diffusion for the prior step with a pretrained denoiser and a lightweight deep-unfolded network for the likelihood step. Experiments on nonlinear phase retrieval show that this alternative reduces likelihood-update cost while maintaining effectiveness compared to MCMC-based split Gibbs.

By Yi Zhang, Rui Guo, Mengchu Xu, Zhaofeng Liu, Yonina C. Eldar
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arXiv Machine Learning
4d ago

Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors

The paper introduces RED-KLwSGS, a new posterior sampling method for Bayesian imaging inverse problems that combines exact Gaussian updates for the data variable with underdamped (kinetic) Langevin diffusion for the auxiliary variable, driven by a one‑shot denoising score. It achieves the same per‑iteration cost as existing Langevin‑within‑SGS samplers while providing non‑asymptotic Wasserstein‑2 convergence guarantees for strongly log‑concave priors. A further variant, Joint-RED-KLwSGS, applies kinetic Langevin diffusion to both variables, and experiments using denoising diffusion probabilistic models on FFHQ and ImageNet demonstrate faster convergence and high‑quality image reconstruction.

By Dai Hai Nguyen, Duc Dung Nguyen
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arXiv AI
Sep 4

A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors

The paper introduces a Posterior‑Dynamics Framework that leverages pretrained diffusion models as multiscale priors for linear imaging inverse problems such as deblurring, super‑resolution, and inpainting. By constructing a surrogate likelihood centered on the clean image and incorporating diffusion uncertainty, the authors derive continuous posterior dynamics and a tunable Langevin component for adaptive exploration. They prove theoretical guarantees (endpoint consistency, finite‑horizon tracking, weak accuracy) and present the PD‑IMEX sampler, which achieves high‑quality reconstructions with only 100 score evaluations and controllable fidelity‑diversity trade‑offs.

By Zhaoqiang Liu, Tongyao Pang, Ruibing Wang, Yang Zheng
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