Provable Mixed-Noise Learning with Flow-Matching
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909849984434176 |
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| author | Hagemann, Paul Gruhlke, Robert Stankewitz, Bernhard Schillings, Claudia Steidl, Gabriele |
| author_facet | Hagemann, Paul Gruhlke, Robert Stankewitz, Bernhard Schillings, Claudia Steidl, Gabriele |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Provable Mixed-Noise Learning with Flow-Matching Hagemann, Paul Gruhlke, Robert Stankewitz, Bernhard Schillings, Claudia Steidl, Gabriele Machine Learning Optimization and Control 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. |
| title | Provable Mixed-Noise Learning with Flow-Matching |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2508.18122 |