mlsanityData to 7 Oct 2026

A Gibbs posterior sampler for inverse problem based on prior diffusion model

arXiv 2602.11059 ↗First posted 11 Feb 2026stat.ML cs.LG stat.APcited by 1

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

Abstract (arXiv)

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive error, (2) the problem is ill-posed and regularization relies on a Bayesian strategy, (3)~the prior is modeled by a diffusion process adjusted on an available large set of examples. In this context, it is known that the issue of posterior sampling is a thorny one and the paper introduces a Gibbs algorithm. It appears that this avenue has not been explored, and we show that it is particularly effective and remarkably simple. In addition, it provides clear elements regarding convergence guarantees in a specific case and arguments supporting such guarantees in practical cases. The results are clearly confirmed by numerical simulations based on a toy example.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. Builds on 8 of its 26 references that are in the map. First posted on arXiv 11 Feb 2026.

Builds on

8 of 26 references.

Closest ancestors · 4

Same direction, newest first

  1. 2024Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling13 Sep
  2. 2024Think Twice Before You Act: Improving Inverse Problem Solving With MCMC13 Sep
  3. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problems15 Aug
  4. 2022Diffusion Posterior Sampling for General Noisy Inverse Problems29 Sep

Other references · 4

  1. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  2. 2024Tutorial on Diffusion Models for Imaging and Visioncited by 49
  3. 2023Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inferencecited by 41
  4. 2024Evaluating the Posterior Sampling Ability of Plug&Play Diffusion Methods in Sparse-View CTcited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Estimation of instrument and noise parameters for inverse problem based on prior diffusion modelcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Mixture-Based Framework for Guiding Diffusion Models
  2. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priors
  3. 2025Diffusion models for inverse problems
  4. 2026Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
  5. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
  6. 2025Solving Diffusion Inverse Problems with Restart Posterior Sampling
  7. 2023GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration
  8. 2026Provable diffusion-based posterior sampling for linear inverse problems via DDIM