{
  "abstract": "High-dimensional count data arise in applications such as single-cell RNA sequencing and neural spike trains, where mappings between distributions across successive batches or time points form critical components of data analysis. The recent success of diffusion- and flow-based deep generative models for images, video, and text motivates extending these ideas to count-valued settings, but many existing methods either treat each count as a categorical state or transform counts into a continuous space, neither of which is natural or efficient when the count range is large. We propose count-FM, a flow-matching framework for count data based on a continuous-time birth-death process with local unit jumps. Count-FM learns marginal transitions efficiently in count space through simulation-free training of conditional transition rates, allowing transport between arbitrary count-distributed source and target populations. In simulation, count-FM variants achieve strong sample quality while using substantially fewer parameters. We further apply count-FM to scRNA-seq and neural spike-train data for unconditional generation, transport, and conditional generation. Across these tasks, count-FM yields improved sample quality, greater modeling efficiency, and interpretable transport paths.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.07746",
  "author_total": 2,
  "authors": [
    {
      "name": "Ganchao Wei"
    },
    {
      "name": "John Pearson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/btckkqz54abgt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.07746",
  "fulltext_url": null,
  "id": "btckkqz54abgt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.07746",
  "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",
      "q-bio.QM"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1312|Single-cell and spatial transcriptomics"
    ]
  ],
  "openalex": "W7160877572",
  "pdf_url": "https://arxiv.org/pdf/2605.07746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/btckkqz54abgt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:44Z",
      "native_id": "2605.07746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.07746"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "arxiv:q-bio.QM",
      "subfield": "bioinformatics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Flow Matching for Count Data",
  "title_text": "Flow Matching for Count Data",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/btckkqz54abgt",
  "venue": "arXiv",
  "versions": []
}