{
  "abstract": "Deciding whether two samples come from the same distribution is a classical problem in statistics, and generative transport offers a new way to approach it. We build a stochastic interpolant directly between the two samples and observe that, for a symmetric schedule, its law is invariant under the time reflection $t \\mapsto 1-t$ whenever the two distributions coincide. We therefore test whether the marginals at times t and 1-t agree by computing their Jensen--Shannon divergence. Both marginals are explicit mixtures over all cross-pairs of observations, so nothing is learned, and permutation calibration gives an exact finite-sample level. For Gaussian noise, this divergence equals a time integral that pairs the reflection defects of the velocity field and of the score, so the test compares transport dynamics rather than endpoints alone. With a narrow-plus-broad noise design, the test attains the minimax separation rate n^{-2s/(4s+d)} over bounded, compactly supported densities whose difference has Sobolev smoothness s > 3d/4, with no lower bound on the densities. Fusing a dyadic grid of noise scales through their permutation ranks, without sample splitting, preserves exact level and adapts to unknown s at an iterated-logarithmic cost. Empirically, the test matches or outperforms state-of-the-art kernel two-sample tests.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08277",
  "author_total": 3,
  "authors": [
    {
      "name": "Eshant English"
    },
    {
      "name": "Kenji Fukumizu"
    },
    {
      "name": "Taiji Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/998z1nxa46aq4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08277",
  "fulltext_url": null,
  "id": "998z1nxa46aq4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08277",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7221013326",
  "pdf_url": "https://arxiv.org/pdf/2610.08277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/998z1nxa46aq4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:32Z",
      "native_id": "2610.08277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08277"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Two-Sample Testing via Generative Processes",
  "title_text": "Two-Sample Testing via Generative Processes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:32Z",
  "url": "https://research.draconitic.com/paper/998z1nxa46aq4",
  "venue": "arXiv",
  "versions": []
}