{
  "abstract": "Flow matching has emerged as a powerful framework for generative modeling, enabling the learning of continuous-time vector fields that transport probability distributions from simple source distributions toward complex target distributions. However, conventional flow-matching systems primarily learn the transformation that generates data, while their model architectures, vector-field parameterizations, probability paths, conditioning mechanisms, and sampling strategies are generally determined through separate design or optimization procedures. This paper proposes Meta-Flow Matching (Meta-FM) as a framework in which flow matching operates not only at the data-generation level but also at the model-construction level. Instead of treating a flow-matching model as a fixed generative mechanism, Meta-FM treats flow-matching models as objects that can themselves be generated, adapted, combined, and optimized through a higher-order flow-matching process.\n\nWe formalize a hierarchy comprising a data-level flow, a model-level flow, and an optional mechanism-level flow. The data-level flow transforms latent samples into generated outputs. The model-level flow transforms an initial representation of a generative model into a task-adapted flow-matching model. The mechanism-level flow can further transform representations of the procedures responsible for constructing and adapting those models. We introduce a task-conditioned meta-vector field, a model-space state representation, an objective combining generative quality and computational costs, and a constrained optimization procedure for higher-order model adaptation. We distinguish this proposal from conventional flow matching, hypernetwork-based generation, neural architecture search, and existing work on Meta Flow Matching, which studies distribution-level dynamics on the Wasserstein manifold. The central distinction proposed here is the use of a learned flow-matching process to construct or adapt flow-matching models themselves.\n\nThis paper establishes a conceptual and mathematical framework rather than an empirically validated method. It identifies implementation requirements, theoretical questions, evaluation protocols, and falsifiable hypotheses necessary to determine whether higher-order flow matching can improve adaptation efficiency, model reuse, and generative performance across related tasks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Jincheng Zhang",
      "orcid": "0009-0005-1860-0009"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7rq35kdtgnq8a.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23530011",
  "fulltext_url": null,
  "id": "7rq35kdtgnq8a",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23530011",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://zenodo.org/api/records/23530011/files/Meta-Flow%20Matching.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7rq35kdtgnq8a.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:21:15Z",
      "native_id": "23530011",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23530011"
    }
  ],
  "subjects": [],
  "title": "Meta-Flow Matching: A Framework for Generating, Adapting, and Optimizing Flow-Matching Models Through Higher-Order Flow Matching",
  "title_text": "Meta-Flow Matching: A Framework for Generating, Adapting, and Optimizing Flow-Matching Models Through Higher-Order Flow Matching",
  "type": "preprint",
  "updated_at": "2026-11-04T12:21:15Z",
  "url": "https://research.draconitic.com/paper/7rq35kdtgnq8a",
  "venue": "Zenodo",
  "versions": []
}