{
  "abstract": "Denoising diffusion probabilistic models (DDPMs) have emerged as a powerful framework for generative modeling by transforming standard Gaussian inputs into outputs that approximate a target distribution. While DDPMs have been proved to converge in total variation, KL divergence, and Wasserstein distance, these discrepancy measures share a fundamental limitation of being insensitive to distributional mismatch in low-probability regions. To address this, we adopt the stronger Rényi divergence as the discrepancy measure. Leveraging a Girsanov-type change-of-measure argument, we establish the first Rényi characterization of DDPMs to the best of our knowledge, showing that the total error decomposes into a mixing error, a discretization error, and a score estimation error. We assume the target distribution is sub-Gaussian and characterize the score error via the cumulant generating function, relaxing both the log-Sobolev-inequality and $L^\\infty$-score-error conditions used in prior Rényi divergence analyses of inexact Langevin Monte Carlo, a score-based sampling algorithm closely related to DDPM. Our results also establish an iteration complexity for achieving $ε$-accuracy in $α$-Rényi divergence that is asymptotically proportional to $α^3/ε$. Finally, by extending our analysis, we establish the first Rényi divergence convergence guarantee for critically damped DDPMs, a kinetic variant governed by critically damped Langevin dynamics. Similar to existing characterizations of critically damped DDPMs, this result shares the structural scaling of standard DDPMs, differing by at most a logarithmic factor in the mixing error exponent, and supports the conjecture that critically damped DDPMs do not yield a theoretical improvement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24984",
  "author_total": 6,
  "authors": [
    {
      "name": "Wenliang Liu"
    },
    {
      "name": "Santiago Mazuelas"
    },
    {
      "name": "Guanding Yu"
    },
    {
      "name": "Renjie Liao"
    },
    {
      "name": "Lele Wang"
    },
    {
      "name": "Yuan Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n0ey12w36801.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24984",
  "fulltext_url": null,
  "id": "7n0ey12w36801",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24984",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7223052123",
  "pdf_url": "https://arxiv.org/pdf/2610.24984",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7n0ey12w36801.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24984",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24984"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2613|Markov Chains and Monte Carlo Methods",
      "subfield": "statistics"
    }
  ],
  "title": "Convergence of Denoising Diffusion Probabilistic Models: A Rényi Divergence Perspective",
  "title_text": "Convergence of Denoising Diffusion Probabilistic Models: A Rényi Divergence Perspective",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7n0ey12w36801",
  "venue": "arXiv",
  "versions": []
}