{
  "abstract": "Existing approaches to differential privacy in diffusion models rely on loose sensitivity bounds and isotropic Gaussian noise, leading to unnecessary estimation error. We develop a framework for the optimal privacy-utility tradeoff of ideal diffusion denoisers, replacing conservative bounds with exact sensitivity characterizations and provably optimal noise calibration. First, we show that worst-case sensitivity over datasets of arbitrary size can be characterized exactly using only two records. For a data domain of size $m$, this reduces the analysis to at most $m(m-1)$ constraints, regardless of dataset size. Our characterization can be arbitrarily tighter than conventional diameter-based sensitivity bounds, revealing potentially unbounded improvements in noise calibration. Second, we obtain exact privacy guarantees for Rényi, approximate, and Gaussian differential privacy, as well as mutual-information privacy for binary records, avoiding the looseness of previous generic privacy conversions. Finally, we show that the minimum achievable weighted mean-squared error can be computed through a semidefinite program and prove strong duality, providing certificates of global optimality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28991",
  "author_total": 2,
  "authors": [
    {
      "name": "Tue Do"
    },
    {
      "name": "Daniel Alabi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ej6cmbghwzvw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28991",
  "fulltext_url": null,
  "id": "4ej6cmbghwzvw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28991",
  "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.CR"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7223221201",
  "pdf_url": "https://arxiv.org/pdf/2610.28991",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ej6cmbghwzvw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28991",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28991"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Diffusion Sensitivity Geometry and Strong Duality for Optimal Privacy-Utility Tradeoffs",
  "title_text": "Diffusion Sensitivity Geometry and Strong Duality for Optimal Privacy-Utility Tradeoffs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/4ej6cmbghwzvw",
  "venue": "arXiv",
  "versions": []
}