This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a prior density, and (3) the latter 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. This paper introduces a Gibbs algorithm. It appears that this avenue has not been explored, and we show that this approach is particularly effective and remarkably simple. In addition, it offers a guarantee of convergence in a clearly identified situation. The results are clearly confirmed by numerical simulations.
@article{arxiv.2602.11059,
title = {A Gibbs posterior sampler for inverse problem based on prior diffusion model},
author = {Jean-François Giovannelli},
journal= {arXiv preprint arXiv:2602.11059},
year = {2026}
}