Perron--Frobenius Operator Matching for Generative Modeling
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 iden...
| Authors | Shiqi Zhang, Wuwei Wu, Jaemin Oh et al. |
|---|---|
| Primary category | cs.LG |
| Published | 16 June 2026 |
| Last updated at source | 16 June 2026 |
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