{
  "abstract": "We establish finite-sample guarantees for conditional diffusion models learned from data and implemented with finitely many denoising steps. Our approach aligns the score-training objective with the sampling grid, allowing statistical estimation and numerical discretization errors to be analyzed together. Under a smooth conditional density model, we derive high-probability bounds on the generated distribution's error and quantify the required number of score evaluations. For every smoothness index $β>0$, a suitable grid yields averaged conditional Kullback--Leibler (KL) divergence $\\widetilde O_p(n^{-2β/(d_x+d_y+2β)})$ relative to the original target with or without early stopping. Both the full and early-stopped samplers attain average target total-variation (TV) error $\\widetilde O_p(n^{-β/(d_x+d_y+2β)})$. Here $n$ is the sample size, $d_x,d_y$ are the data and conditioning dimensions, and errors are averaged over the conditioning variable. The total-variation bound matches the rate established in existing conditional distribution-estimation theory, up to logarithmic factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13851",
  "author_total": 1,
  "authors": [
    {
      "name": "Qiuyun Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/579mqkcret3ej.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13851",
  "fulltext_url": null,
  "id": "579mqkcret3ej",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13851",
  "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": "W7221508438",
  "pdf_url": "https://arxiv.org/pdf/2610.13851",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/579mqkcret3ej.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:46Z",
      "native_id": "2610.13851",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13851"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models",
  "title_text": "Finite-Sample Guarantees for Fully Discrete Conditional Diffusion Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:46Z",
  "url": "https://research.draconitic.com/paper/579mqkcret3ej",
  "venue": "arXiv",
  "versions": []
}