{
  "abstract": "Although score-based generative models (SGMs) have achieved remarkable success in real-world sample generation tasks, it is still far from sufficient to understand them from a mathematical perspective. In this paper, we aim to provide enhanced convergence guarantees for two existing SGMs in $\\mathcal{W}_2$-distance beyond log-concavity. More precisely, we develop a novel framework of {\\color{black}discretization} error analysis for Euler-Maruyama (EM) and Poisson midpoint (PM) time discretization schemes for SGMs. Under a non-log-concavity condition, we show that $\\tilde{\\mathcal{O}}(\\sqrt{d}/ε)$ iterations suffice to approximate the target distributions in $ε$-accuracy for the classical EM-based SGM, considerably improving upon the existing iteration complexity $\\tilde{\\mathcal{O}}(d/ε^2)$. Notably, the novel framework of error analysis also enables us to establish an $\\tilde{\\mathcal{O}}(\\sqrt{d}/ε^{2/3})$ iteration complexity for the PM-based SGM in $ε$-accuracy, significantly outperforming current state-of-the-art Wasserstein convergence guarantees for SDE-based diffusion samplers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40308",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiaoyan Zhang"
    },
    {
      "name": "Chenxu Pang"
    },
    {
      "name": "Xiaojie Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/676jz8rgxnd0y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40308",
  "fulltext_url": null,
  "id": "676jz8rgxnd0y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40308",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40308",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/676jz8rgxnd0y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40308",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40308"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Enhanced convergence guarantees of score-based generative models in $\\mathcal{W}_2$-distance beyond log-concavity",
  "title_text": "Enhanced convergence guarantees of score-based generative models in 𝒲_2-distance beyond log-concavity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/676jz8rgxnd0y",
  "venue": "arXiv",
  "versions": []
}