arXiv Machine Learning
Jun 30

Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences

arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.

By Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang