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arXiv · 2606.17465

Perron--Frobenius Operator Matching for Generative Modeling

Shiqi Zhang·Wuwei Wu·Jaemin Oh·Jie Chen·Xiaoning Qian
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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.

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Shiqi Zhang, Wuwei Wu, Jaemin Oh, Jie Chen, Xiaoning Qian. 2026-06-16. Perron--Frobenius Operator Matching for Generative Modeling. https://arxiv.org/abs/2606.17465

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