{
  "abstract": "Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce numerical integration cost. Yet, the population-level coupling induced by repeated minibatch OT remains only partially understood. We formalize this coupling as the expected batch OT plan $\\overlineπ_{k}$, obtained by averaging empirical OT plans over independent minibatches of size $k$. We then establish its large-batch consistency and, in the semidiscrete case relevant to generative modeling, derive rates for both the transport-cost bias and the convergence of $\\overlineπ_{k}$ to the OT plan. For FM, this yields a population coupling whose induced velocity field is regular enough to define a unique flow from the source to the discrete target. We finally quantify how OT batch size interacts with numerical integration in a tractable two-atom model and in synthetic and image experiments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12174",
  "author_total": 3,
  "authors": [
    {
      "name": "Samuel Boïté"
    },
    {
      "name": "Julie Delon"
    },
    {
      "name": "Kimia Nadjahi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4psd5e7rpvjze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12174",
  "fulltext_url": null,
  "id": "4psd5e7rpvjze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12174",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7161017294",
  "pdf_url": "https://arxiv.org/pdf/2605.12174",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4psd5e7rpvjze.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2605.12174",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12174"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Expected Batch Optimal Transport Plans and Consequences for Flow Matching",
  "title_text": "Expected Batch Optimal Transport Plans and Consequences for Flow Matching",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/4psd5e7rpvjze",
  "venue": "arXiv",
  "versions": []
}