Perron--Frobenius Operator Matching for Generative Modeling
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Computer Science > Machine Learning
Title:Perron--Frobenius Operator Matching for Generative Modeling
Abstract:We introduce Perron--Frobenius Operator Matching (PFOM), a generative framework that matches density evolution via the integral PF operator, subsuming flow, diffusion, and jump models. We prove that among Bregman divergences, only Kullback--Leibler divergence preserves equality between density-level and sample-conditioned objectives, yielding a practical loss equivalent to Koopman path matching. We further develop Nesterov-accelerated training and sampling that stabilize discretization and accelerate convergence. %On Gaussian mixtures and two-moons, PFOM achieves faster KL/$W_2$/MMD decrease and improved wall-clock efficiency with empirical validation. PFOM unifies operator-theoretic identification with modern generative modeling and opens paths to adaptive dictionaries and high-dimensional applications.
| Subjects: | Machine Learning (cs.LG); Systems and Control (eess.SY) |
| Cite as: | arXiv:2606.17465 [cs.LG] |
| (or arXiv:2606.17465v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.17465
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