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

Jean-François Giovannelli
2/11/2026
stat.MLcs.LGstat.AP

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Abstract

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.

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Cite this paper

@article{giovannelli2026gibbs,
  title  = {A Gibbs posterior sampler for inverse problem based on prior diffusion model},
  author = {Jean-François Giovannelli},
  year   = {2026},
  eprint = {2602.11059},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2602.11059v1}
}

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