{
  "abstract": "Recent literature has shown a strong connection between optimization and sampling. We develop the corresponding first-order theory for diffusion models. First, the SDE-based reverse-time flows of overdamped and underdamped Langevin diffusions contract relative Fisher divergences at explicit exponential rates whenever the stationary potential of the forward process is strongly convex---a condition on the noising process one chooses, not on the data. This is a unique advantage of SDE-based reverse diffusion, absent in the reverse process based on ODEs. Second, we incorporate discretization and establish averaged first-order stationarity bounds---the sampling analog of averaged gradient-norm guarantees in nonconvex optimization---for samplers of both overdamped and underdamped diffusion models. As in nonconvex optimization, the convexity-free certificate is local: it guarantees score consistency, not global mode weights.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31612",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhifeng Chen"
    },
    {
      "name": "Chenyang Jiang"
    },
    {
      "name": "Yazhen Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4j5ab9wvpq17r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31612",
  "fulltext_url": null,
  "id": "4j5ab9wvpq17r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31612",
  "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|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7214656100",
  "pdf_url": "https://arxiv.org/pdf/2609.31612",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4j5ab9wvpq17r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:03Z",
      "native_id": "2609.31612",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31612"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "First-Order Stationarity of Reverse Diffusions",
  "title_text": "First-Order Stationarity of Reverse Diffusions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:03Z",
  "url": "https://research.draconitic.com/paper/4j5ab9wvpq17r",
  "venue": "arXiv",
  "versions": []
}