{
  "abstract": "Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions. Despite being commonly described as low-likelihood events, existing generative approaches rarely control likelihood explicitly. In this work, we introduce a measure-theoretic notion of outliers based on the distribution of log-likelihood values, which is guaranteed to assign higher probability mass to low-likelihood events with a specifiable magnitude. Building on this formulation, we derive how likelihood reweighting modifies the diffusion score and use this relation to motivate a controlled modification of the reverse-time dynamics. In particular, likelihood reweighting implies a scaling of the score function with a control term derived from the Radon-Nikodym derivative of the likelihood distributions. Correspondingly, the updated score function can be obtained with no retraining of the diffusion model. We exploit the Ornstein-Uhlenbeck semigroup underlying diffusion models to motivate an exponentially interpolated controller which approximates the true control. Experiments demonstrate controlled generation of low-likelihood samples while remaining consistent with the data geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: IEEE Conference on Decision and Control (CDC), 2026",
  "arxiv": "2609.12113",
  "author_total": 5,
  "authors": [
    {
      "name": "Amartya Mukherjee"
    },
    {
      "name": "Tristan Milne"
    },
    {
      "name": "Kry Yik-Chau Lui"
    },
    {
      "name": "Stephanie Hazlewood"
    },
    {
      "name": "Jun Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4k40m7dh4vrb4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12113",
  "fulltext_url": null,
  "id": "4k40m7dh4vrb4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12113",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Adversarial Robustness in Machine Learning"
    ]
  ],
  "openalex": "W7212697042",
  "pdf_url": "https://arxiv.org/pdf/2609.12113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4k40m7dh4vrb4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative",
  "title_text": "Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:17Z",
  "url": "https://research.draconitic.com/paper/4k40m7dh4vrb4",
  "venue": "arXiv",
  "versions": []
}