Mixed Poisson diffusion models and application to posterior sampling
Abstract
Diffusion models are a powerful framework for learning complex probability distributions. While widely used diffusion models for continuous data rely on Gaussian noising processes, we instead develop diffusion models based on Poisson noise. More precisely, we introduce and study a new mathematical framework, called Mixed Poisson Diffusion Models (MPDM), with noising dynamics driven by multivariate counting processes. Our methodology is motivated by Poisson inverse problems. The success of Gaussian diffusion models has led to their use as prior models in a growing number of posterior sampling methods for inverse problems. However, most of these approaches focus on Gaussian inverse problems, in which observations are generated through a deterministic forward operator corrupted by additive Gaussian noise. By contrast, Poisson inverse problems, where observations are discrete and Poisson distributed, remain comparatively underexplored in this literature. Building on our Poisson generative dynamics, we develop a natural framework for posterior sampling in Poisson inverse problems and derive several posterior sampling algorithms based on the proposed model. We evaluate our approach on realistic Poisson inverse problems and show that the resulting framework is well suited to this class of problems.
Related
- Accelerating posterior sampling in Bayesian inverse problems with diffusion models: an online-offline perspective
- Learning to Replace MCMC in Split-Gibbs Diffusion Posterior Sampling via Deep Unfolding
- Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors
- UAV SAR Imaging via Diffusion Posterior Sampling under Non-Ideal Motion in ISAC Systems
- Power-posterior implicit sampling for efficient Bayesian experimental design: Application to contaminant source identification in groundwater flow
BibTeX
@misc{pellerin2026mixed,
title = {{Mixed Poisson diffusion models and application to posterior sampling}},
author = {Thibaut Pellerin and Alain Durmus and Elinor Berger and Eric Barat},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20218},
eprint = {2610.20218},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20218},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mixed Poisson diffusion models and application to posterior sampling
AU - Thibaut Pellerin
AU - Alain Durmus
AU - Elinor Berger
AU - Eric Barat
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20218
UR - https://arxiv.org/abs/2610.20218
AB - Diffusion models are a powerful framework for learning complex probability distributions. While widely used diffusion models for continuous data rely on Gaussian noising processes, we instead develop diffusion models based on Poisson noise. More precisely, we introduce and study a new mathematical framework, called Mixed Poisson Diffusion Models (MPDM), with noising dynamics driven by multivariate counting processes. Our methodology is motivated by Poisson inverse problems. The success of Gaussian diffusion models has led to their use as prior models in a growing number of posterior sampling methods for inverse problems. However, most of these approaches focus on Gaussian inverse problems, in which observations are generated through a deterministic forward operator corrupted by additive Gaussian noise. By contrast, Poisson inverse problems, where observations are discrete and Poisson distributed, remain comparatively underexplored in this literature. Building on our Poisson generative dynamics, we develop a natural framework for posterior sampling in Poisson inverse problems and derive several posterior sampling algorithms based on the proposed model. We evaluate our approach on realistic Poisson inverse problems and show that the resulting framework is well suited to this class of problems.
ER -