arXiv：cs.LG· Thibaut Pellerin, Alain Durmus, Elinor Berger, Eric Barat·· 6 小时前
Mixed Poisson 扩散模型（MPDM）：用于泊松逆问题的后验采样
Mixed Poisson diffusion models and application to posterior sampling
AI 导读
研究者提出 Mixed Poisson 扩散模型（MPDM），一种以多元计数过程驱动加噪动力学的扩散框架，噪声基于 Poisson 分布而非传统高斯噪声，动机来自泊松逆问题。基于该生成动力学，作者为观测离散且服从 Poisson 分布的泊松逆问题构建后验采样框架，并推导出多种后验采样算法。在真实泊松逆问题上的评估显示该框架适配此类问题。
正文
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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Computation (stat.CO) |
| Cite as: | arXiv:2610.20218 [stat.ML] |
| (or arXiv:2610.20218v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.20218 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Thibaut Pellerin [view email]
[v1]
Wed, 14 Oct 2026 13:57:32 UTC (5,956 KB)
来源：arXiv：cs.LG · arxiv.org