{
  "abstract": "We establish arbitrary-order a priori regularity estimates for the reverse heat flow in the Ornstein--Uhlenbeck setting, that is, for the probability-flow ODE of score-based diffusion models. For compactly supported, possibly singular targets satisfying a dimension-uniform doubling condition on supporting-cap masses, we bound the iterated material derivatives of the flow and their first spatial derivatives pointwise, with constants independent of the dimension $d$ and explicit in time and support radius. The proof rests on two ingredients: a spatially uniform bound on normal-direction posterior fluctuations, which is the only point where the geometry of the target enters, and a centered posterior-moment normal form closed under material differentiation. This algebraic structure, together with a weighted regularity calculus, yields quantitative bounds at every order, including the mixed space--time directional derivatives required by Runge--Kutta stages. As an application, for exact-score sampling stopped at forward time $δ>0$, order-$p$ Taylor and explicit Runge--Kutta schemes reach accuracy $\\varepsilon$ in $\\widetilde O(d^{1/p}\\varepsilon^{-1/p})$ steps in total variation, and the Taylor scheme in $\\widetilde O(d^{1/(2p)}\\varepsilon^{-1/p})$ steps in $W_2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24622",
  "author_total": 2,
  "authors": [
    {
      "name": "Xixian Wang"
    },
    {
      "name": "Zhongjian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/an1jkzfwvsgag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24622",
  "fulltext_url": null,
  "id": "an1jkzfwvsgag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24622",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7214016733",
  "pdf_url": "https://arxiv.org/pdf/2609.24622",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/an1jkzfwvsgag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24622",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24622"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A priori regularity of the reverse heat flow and dimension-dependent complexity of higher-order diffusion samplers",
  "title_text": "A priori regularity of the reverse heat flow and dimension-dependent complexity of higher-order diffusion samplers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/an1jkzfwvsgag",
  "venue": "arXiv",
  "versions": []
}