{
  "abstract": "Motivated by the success of modern flow-based generative models in modeling complex data, we study two-sample testing through the lens of flow-based methods. We propose the Zero-Flow Two-Sample Test (ZF2ST), built on the zero-flow criterion, which characterizes distributional equality through a time-reversal antisymmetry of a learnable velocity field. We extend this criterion and further develop the Zero-Flow Discrepancy, an identifying discrepancy that controls the Wasserstein distance, and derive a variational representation in terms of a witness function. This representation naturally leads to a witness-based test whose power is governed by the signal-to-noise ratio (SNR), allowing direct power maximization for witness learning. ZF2ST learns the witness on one data split and performs testing on held-out samples, thereby maintaining Type-I error control and admitting a simple asymptotic null distribution. Experimentally, ZF2ST performs competitively across various synthetic and real-world benchmarks, while showing particularly strong performance in distinguishing image distributions from different sources.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.21542",
  "author_total": 4,
  "authors": [
    {
      "name": "Yakun Wang"
    },
    {
      "name": "Leyang Wang"
    },
    {
      "name": "Song Liu"
    },
    {
      "name": "Taiji Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9a1m25kf702x4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.21542",
  "fulltext_url": null,
  "id": "9a1m25kf702x4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.21542",
  "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",
      "stat.ML"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7170864249",
  "pdf_url": "https://arxiv.org/pdf/2607.21542",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9a1m25kf702x4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:58Z",
      "native_id": "2607.21542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.21542"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Zero-Flow Two-Sample Tests",
  "title_text": "Zero-Flow Two-Sample Tests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:58Z",
  "url": "https://research.draconitic.com/paper/9a1m25kf702x4",
  "venue": "arXiv",
  "versions": []
}