mlsanityData to 7 Oct 2026

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

arXiv 2609.30539 ↗First posted 24 Sep 2026eess.SP cs.LG stat.MLcited by 0

On the map: Diffusion models → Inverse problems and image restoration

Abstract (arXiv)

Split Gibbs sampling enables diffusion posterior inference for general nonlinear inverse problems by decoupling prior and likelihood computations, allowing a pretrained diffusion prior to be reused across measurement models. However, its likelihood update often relies on iterative MCMC, which can hinder parallelization, require algorithm-specific tuning, and incur substantial computational cost. In this work, we propose a learning-based framework to replace this MCMC step by reformulating both Gibbs updates as Gaussian denoising problems and implementing them through ODE diffusion. The prior step reuses a pretrained denoiser, while the likelihood denoiser exploits known likelihood structure through a lightweight deep-unfolded network. Experiments on nonlinear phase retrieval demonstrate the effectiveness of the proposed method as an alternative to MCMC-based split Gibbs at lower likelihood-update cost.

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. Builds on 17 of its 20 references that are in the map. First posted on arXiv 24 Sep 2026.

Builds on

17 of 20 references.

Closest ancestors · 9

Same direction, newest first

  1. 2026Bayesian Signal Component Decomposition via Diffusion-within-Gibbs Sampling11 Feb
  2. 2025Diffusion-Prior Split Gibbs Sampling for Synthetic Aperture Radar Imaging under Incomplete Measurements2 Dec
  3. 2025Bayesian Signal Separation via Plug-and-Play Diffusion-Within-Gibbs Sampling16 Sep
  4. 2025Plug-and-Play Latent Diffusion for Electromagnetic Inverse Scattering with Application to Brain Imaging5 Sep
  5. 2024A Survey on Diffusion Models for Inverse Problems30 Sep
  6. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing1 Jul
  7. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors29 May
  8. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction25 Mar
  9. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 8

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 2,994
  4. 2019Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processingcited by 411
  5. 2018Split-and-augmented Gibbs sampler - Application to large-scale inference problemscited by 47
  6. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  7. 2021Deep Unfolding with Normalizing Flow Priors for Inverse Problemscited by 23
  8. 2025Deep Unfolding: Recent Developments, Theory, and Design Guidelinescited by 7

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  1. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  2. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  3. 2026Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Steps
  4. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  5. 2025A Mixture-Based Framework for Guiding Diffusion Models
  6. 2025Learning few-step posterior samplers by unfolding and distillation of diffusion models
  7. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration
  8. 2025DDRM-PR: Fourier Phase Retrieval using Denoising Diffusion Restoration Models