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

arXiv: https://arxiv.org/abs/2602.11059 · HTML: https://mlsanity.com/paper/2602.11059/

## Key facts

- Cited by 1 papers in the map (data through 14 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.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 8 of 8)

- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Monte Carlo guided Diffusion for Bayesian linear inverse problems](https://mlsanity.com/paper/2308.07983/) (2023)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [Plug-and-Play split Gibbs sampler: embedding deep generative priors in Bayesian inference](https://mlsanity.com/paper/2304.11134/) (2023)
- [Think Twice Before You Act: Improving Inverse Problem Solving With MCMC](https://mlsanity.com/paper/2409.08551/) (2024)
- [Gaussian is All You Need: A Unified Framework for Solving Inverse Problems via Diffusion Posterior Sampling](https://mlsanity.com/paper/2409.08906/) (2024)
- [Evaluating the Posterior Sampling Ability of Plug&Play Diffusion Methods in Sparse-View CT](https://mlsanity.com/paper/2410.21301/) (2024)

## Built on by (most cited first, 1 of 1)

- [Estimation of instrument and noise parameters for inverse problem based on prior diffusion model](https://mlsanity.com/paper/2602.11711/) (2026)

## 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.