{
  "abstract": "Despite their empirical success, why diffusion models overcome the bottlenecks of classical score-based samplers remains unclear. In this work, we leverage Gaussian distributions to isolate this phenomenon. We establish 2-Wasserstein convergence bounds for optimized hyperparameters, showing that diffusion processes achieve a sampling error of $O(\\sqrt{dλ_{\\max}}\\log N/N)$, where $d$ is the dimension, $N$ the number of sampling steps, and $λ_{\\max}$ the largest eigenvalue of the target covariance matrix. Unadjusted and underdamped Langevin dynamics suffer from an additional $\\sqrtκ$ factor, where $κ$ is the condition number. These rates follow from spectral bounds which are sharp: we confirm them via matching first-order asymptotics as $N\\rightarrow\\infty$. Our analysis provides a rigorous characterization, in the Gaussian setting, of how time-dependent score trajectories remove condition-number dependence during sampling. By contrast, in the learning phase, we show that estimating the unnoised score by gradient descent leads to essentially the same estimator as estimating a noisy score, which suggests that the benefits of noising do not come from the learning phase.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12052",
  "author_total": 3,
  "authors": [
    {
      "name": "Adam Perbost"
    },
    {
      "name": "Francis Bach"
    },
    {
      "name": "Pierre Marion"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fvex4dtgzn6c7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12052",
  "fulltext_url": null,
  "id": "fvex4dtgzn6c7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12052",
  "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.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7221076341",
  "pdf_url": "https://arxiv.org/pdf/2610.12052",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fvex4dtgzn6c7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:03Z",
      "native_id": "2610.12052",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12052"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis",
  "title_text": "Diffusion Removes Langevin's Conditioning Dependence: A Sharp Gaussian Analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/fvex4dtgzn6c7",
  "venue": "arXiv",
  "versions": []
}