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.

翻译：我们研究具有混合噪声的贝叶斯逆问题，该噪声建模为加性与乘性高斯分量的组合。虽然传统推断方法通常假设噪声特性固定或已知，但现实应用（尤其在物理与化学领域）常涉及具有未知异质结构的噪声。受基于流的生成建模最新进展启发，我们提出一种新颖的推断框架，该框架将条件流匹配嵌入期望最大化算法中，以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，我们在EM算法的E步中采用基于无模拟常微分方程的流匹配作为生成模型。我们证明，在适当假设下，EM更新在无限观测的总体极限中收敛至真实噪声参数。数值结果表明，将EM推断与流匹配相结合能有效处理混合噪声贝叶斯逆问题。