Provable Mixed-Noise Learning with Flow-Matching
This addresses noise estimation challenges in physics and chemistry applications, but it is incremental as it builds on existing flow-based and EM methods.
The paper tackles Bayesian inverse problems with mixed additive and multiplicative Gaussian noise by proposing a novel inference framework that combines conditional flow matching with an Expectation-Maximization algorithm to jointly estimate posterior samplers and noise parameters. It proves convergence to true noise parameters under assumptions and demonstrates effectiveness numerically.
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.