{
  "abstract": "Gaussian diffusion models offer a practical framework for generative modeling. Denoising Lévy Probabilistic Models (DLPM) introduce heavy-tailed perturbations with a fixed tail index throughout denoising. We introduce Annealed Lévy Diffusion (ALD). ALD varies the stability index $α(t)$ to combine heavy-tailed exploration with Gaussian refinement. Our marginal-first formulation represents stable noise as a scalar Gaussian scale mixture. This formulation enables standard Gaussian noise-prediction training with one additional scale input. We study two sampling processes. ALD-renoise estimates the clean sample and injects fresh marginal noise. ALD-posterior preserves dependence between successive states through an accumulated conditional variance and a Gaussian bridge update. Both samplers reuse the same trained predictor with different scalar inputs. We evaluate ALD on four 2D benchmarks and an imbalanced nine-mode mixture. We also examine training efficiency and the effects of prediction perturbations on clipped Holtsmark data. Additional experiments evaluate MNIST and CelebA64 generation and CIFAR-10LT augmentation. ALD preserves local geometry on the evaluated light-tailed and manifold-structured targets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19692",
  "author_total": 5,
  "authors": [
    {
      "name": "Yuling Jiao"
    },
    {
      "name": "Lican Kang"
    },
    {
      "name": "Jerry Zhijian Yang"
    },
    {
      "name": "Cheng Yuan"
    },
    {
      "name": "Ruizhe Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3hand70z0t16.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19692",
  "fulltext_url": null,
  "id": "b3hand70z0t16",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19692",
  "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",
      "1707|Generative Adversarial Networks and Image Synthesis"
    ]
  ],
  "openalex": "W7221887920",
  "pdf_url": "https://arxiv.org/pdf/2610.19692",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3hand70z0t16.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19692",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19692"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics",
  "title_text": "Annealed Lévy Diffusion via Gaussian Surrogate Reverse Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/b3hand70z0t16",
  "venue": "arXiv",
  "versions": []
}