---
title: "Point interpolation and distributional universality in flow-based generative models"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2611.04207v1"
permalink: "https://feed.astralor.com/items/itm_ea2f96b2b6b3f5a014d152b4"
published: "2026-11-03T02:44:44.000Z"
score: 56
channel: "ai"
tags: ["Point","Motivated","Lipschitz","For Wasserstein","For","Sobolev"]
---

# Point interpolation and distributional universality in flow-based generative models

## At a glance

Motivated by the expressive power of neural ordinary differential equations in flow-based generative modeling, we study the approximation of probability measures by pushforwards generated by parameterized families of Li…

## Key points

- Motivated by the expressive power of neural ordinary differential equations in flow-based generative modeling, we study the approximation of probability measures by pushforwards generated by parameterized families of Li…
- For Wasserstein distances, we establish a quantitative relationship between finite-sample point interpolation and distributional approximation, and derive universality criteria based on $L^p$-approximation of transport …
- In particular, affine-invariant families containing a non-affine vector field are universal from compactly supported absolutely continuous base measures.

## Full text

Motivated by the expressive power of neural ordinary differential equations in flow-based generative modeling, we study the approximation of probability measures by pushforwards generated by parameterized families of Lipschitz vector fields. For Wasserstein distances, we establish a quantitative relationship between finite-sample point interpolation and distributional approximation, and derive universality criteria based on $L^p$-approximation of transport maps. In particular, affine-invariant families containing a non-affine vector field are universal from compactly supported absolutely continuous base measures. For total variation, we show that coordinate-wise dynamics are insufficient in dimensions $d\geq 2$ and establish sufficient conditions based on one-dimensional Sobolev approximation and shear-type mixing. We further examine the role of point interpolation, establishing when different regimes relate to one another and when approximate interpolation can be made exact.

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