{
  "abstract": "We study generative bootstrap processes obtained by resampling from fitted generative distributions. We establish necessary and sufficient conditions for their conditional weak convergence to the $P$-Brownian bridge, formulated in terms of finite-dimensional conditional weak convergence and conditional asymptotic equicontinuity. We further provide general sufficient conditions and a Giné-Zinn-type characterization relating this convergence to the $P$-Donsker property. As applications, we verify these conditions for prominent classes of generative models, including triangular normalizing flows, flow matching, score-based diffusion models, and Wasserstein generative adversarial networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13471",
  "author_total": 2,
  "authors": [
    {
      "name": "Ziming Lin"
    },
    {
      "name": "Fang Han"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5kbc8bwtvyqnj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13471",
  "fulltext_url": null,
  "id": "5kbc8bwtvyqnj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13471",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1707|Generative Adversarial Networks and Image Synthesis"
    ]
  ],
  "openalex": "W7213313042",
  "pdf_url": "https://arxiv.org/pdf/2609.13471",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5kbc8bwtvyqnj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13471",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13471"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Generative bootstrap processes",
  "title_text": "Generative bootstrap processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/5kbc8bwtvyqnj",
  "venue": "arXiv",
  "versions": []
}