A Gibbs posterior sampler for inverse problem based on prior diffusion model
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914323227475968 |
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| author | Giovannelli, Jean-François |
| author_facet | Giovannelli, Jean-François |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Gibbs posterior sampler for inverse problem based on prior diffusion model Giovannelli, Jean-François Machine Learning Applications 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. |
| title | A Gibbs posterior sampler for inverse problem based on prior diffusion model |
| topic | Machine Learning Applications |
| url | https://arxiv.org/abs/2602.11059 |