{
  "abstract": "In many high-stakes domains, extreme events carry substantial consequences, yet learning the heavy-tailed distributions that govern them from finite samples remains challenging: the quantities of interest are driven by a few extreme observations, so the tail is under-sampled relative to its importance. Even generative models tailored for heavy tails capture the tail region inadequately in practice. We propose the Conditional Value-at-Risk (CVaR)-penalized Generative Particle Algorithm (CVaR-GPA), a tail-agnostic algorithm for fine-tuning generative models toward heavy-tailed targets, built as a time discretization of the Wasserstein gradient flow of the Lipschitz-regularized KL divergence penalized by a CVaR discrepancy term. Such a flow can be initialized from the output samples of the pre-trained model, which are then transported along the gradient descent of the loss functional, without requiring access to the pre-trained model's internal architecture. The Lipschitz-regularized KL divergence requires minimal assumptions on the target, while the CVaR penalty focuses the flow on the tail. The CVaR penalty depends on the target only through a scalar tail statistic, inducing a velocity field that remains active in the under-sampled tail region at a dimension-free estimation cost. The resulting velocity field, and hence the depth of the transport map, implicitly adapts to the target, without target-specific modifications. Across four targets, including two real-world, high-dimensional datasets (daily streamflow in the Ohio River basin ($d=64$) and the Fama-French portfolios ($d=25$) with tail indices ranging from $1.05$ to $3.34$), fine-tuning with CVaR-GPA reduces global and tail errors by geometric-mean factors of $14.0 \\times$ and $9.8 \\times$, respectively, across seven pre-trained models spanning GANs, diffusion models, and other generative flows, with a single set of hyperparameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11544",
  "author_total": 6,
  "authors": [
    {
      "name": "Thejani Gamage"
    },
    {
      "name": "Hyemin Gu"
    },
    {
      "name": "Zhizhen Zhang"
    },
    {
      "name": "Ziyu Chen"
    },
    {
      "name": "Markos A. Katsoulakis"
    },
    {
      "name": "Luc Rey-Bellet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83hqkxahsp948.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11544",
  "fulltext_url": null,
  "id": "83hqkxahsp948",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11544",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1707|Generative Adversarial Networks and Image Synthesis"
    ]
  ],
  "openalex": "W7202390759",
  "pdf_url": "https://arxiv.org/pdf/2608.11544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83hqkxahsp948.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:56Z",
      "native_id": "2608.11544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11544"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows",
  "title_text": "Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/83hqkxahsp948",
  "venue": "arXiv",
  "versions": []
}