{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04207",
  "author_total": 4,
  "authors": [
    {
      "name": "Antonio Álvarez-López"
    },
    {
      "name": "Jingpu Cheng"
    },
    {
      "name": "Liyan Zhang"
    },
    {
      "name": "Qianxiao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f5gn5rmgj731s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04207",
  "fulltext_url": null,
  "id": "f5gn5rmgj731s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04207",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04207",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f5gn5rmgj731s.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04207",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04207"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Point interpolation and distributional universality in flow-based generative models",
  "title_text": "Point interpolation and distributional universality in flow-based generative models",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:10Z",
  "url": "https://research.draconitic.com/paper/f5gn5rmgj731s",
  "venue": "arXiv",
  "versions": []
}