{
  "abstract": "Score-based generative models driven by α-stable Lévy processes have been proposed as an alternative to Brownian diffusion models, with empirical evidence suggesting improved sampling and better modeling of heavy-tailed data. Yet theoretical guarantees for these models remain limited. We develop a non-asymptotic convergence analysis for scale-preserving α-stable generative dynamics, covering both compactly supported and power-law targets. In p-Wasserstein distance, we quantify the effects of early stopping, initialization, score approximation, and time discretization, and show exponential decay of the initialization error. A comparison with Brownian dynamics reveals that global Wasserstein convergence alone does not fundamentally distinguish the two models: both initialization errors decay exponentially with the forward horizon on the common class of heavy-tailed targets. A sharp separation emerges instead in the tails. At any positive generation time, stable dynamics produces power-law tails with index α, whereas Brownian dynamics remains light-tailed. For a target with tail index ν, asymptotically correct extreme-quantile scaling is possible precisely when α=ν. These results identify tail-index matching as a principled mechanism behind the ability of stable generative models to capture extreme events.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19773",
  "author_total": 2,
  "authors": [
    {
      "name": "Ianis Hammani"
    },
    {
      "name": "Claire Boyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avw5dm8hmg4f0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19773",
  "fulltext_url": null,
  "id": "avw5dm8hmg4f0",
  "issns": [],
  "landing_url": "https://hal.science/hal-05790341v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
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      "arxiv",
      "math.PR"
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      "arxiv",
      "stat.ML"
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      "1.info.info-lg"
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      "1.math.math-pr"
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      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
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  "openalex": "W7222215696",
  "pdf_url": "https://hal.science/hal-05790341/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avw5dm8hmg4f0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:53Z",
      "native_id": "hal-05790341",
      "source": "hal",
      "url": "https://hal.science/hal-05790341v1"
    },
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19773",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19773"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "From Global to Tail Convergence: Dynamics of α-Stable Score-Based Generative Models",
  "title_text": "From Global to Tail Convergence: Dynamics of α-Stable Score-Based Generative Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/avw5dm8hmg4f0",
  "venue": "HAL",
  "versions": []
}