Expressivity of Bi-Lipschitz Normalizing Flows: A Score-Based Diffusion Perspective
Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based diffusion models. For the probability flow ODE of a variance-preserving diffusion, Lipschitz regularity of the score induces a flow of bi-Lipschitz diffeomorphic transport maps. This ODE bridge allows us to analyze the distributional approximation power of bi-Lipschitz normalizing flows and, conversely, derive deterministic convergence guarantees for diffusion-based transport. Our key idea is to use the probability flow ODE to link regularity of the score...
| Authors | Meira Iske, Carola-Bibiane Schönlieb |
|---|---|
| Primary category | stat.ML |
| Published | 7 May 2026 |
| Last updated at source | 7 May 2026 |
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