用流模型联合估计噪声与后验，解决真实场景下的混合噪声反问题。
Provable Mixed-Noise Learning with Flow-Matching
- 基于条件流匹配的EM算法，同步优化噪声参数与后验采样器。
- 在无限观测下，证明了噪声参数可收敛到真实值。
- 适合物理、化学等含未知混合噪声的高维反演任务。
我们研究混合噪声下的贝叶斯逆问题，噪声由加性与乘性高斯成分构成。传统方法常假设噪声特性已知，但真实世界（如物理、化学）中的噪声结构往往未知且异质。受流生成模型进展启发，提出一种新型推断框架：将条件流匹配嵌入期望最大化（EM）算法中，联合估计后验采样器与噪声参数。为实现高维推断并提升可扩展性，在EM的E步中采用无模拟的基于常微分方程的流匹配作为生成模型。在合理假设下，证明了当观测无限多时，EM更新收敛至真实噪声参数。数值实验表明，结合EM与流匹配在混合噪声贝叶斯逆问题上有效。
原文摘要 · Abstract (English)
We study Bayesian inverse problems with mixed noise, modeled as a combination of additive and multiplicative Gaussian components. While traditional inference methods often assume fixed or known noise characteristics, real-world applications, particularly in physics and chemistry, frequently involve noise with unknown and heterogeneous structure. Motivated by recent advances in flow-based generative modeling, we propose a novel inference framework based on conditional flow matching embedded within an Expectation-Maximization (EM) algorithm to jointly estimate posterior samplers and noise parameters. To enable high-dimensional inference and improve scalability, we use simulation-free ODE-based flow matching as the generative model in the E-step of the EM algorithm. We prove that, under suitable assumptions, the EM updates converge to the true noise parameters in the population limit of infinite observations. Our numerical results illustrate the effectiveness of combining EM inference with flow matching for mixed-noise Bayesian inverse problems.
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