{
  "abstract": "Drifting models offer a promising route to faster generative AI: they perform gradual transport during training, while generating new samples in a single step. This paper asks whether the underlying drifting process can converge rapidly to a target distribution under ideal conditions, before finite-data or optimization effects are introduced. We show that its convergence rate depends critically on how it handles spatial scale. With a single fixed resolution, fine-scale features of the target can become nearly invisible, leading to extremely slow convergence. We introduce a multihead approach that combines scale-normalized information across a continuum of resolutions. We prove that this multihead approach restores exponential convergence near standard reference distributions. These results identify fixed resolution as a key bottleneck and provide a simple route to faster one-step generative models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Arthur Stéphanovitch"
    },
    {
      "name": "Eddie Aamari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6b5ysf1n3nmcg.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "6b5ysf1n3nmcg",
  "issns": [],
  "landing_url": "https://hal.science/hal-05760108v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.stat"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
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      "hal",
      "1.stat.ml"
    ]
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05760108/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6b5ysf1n3nmcg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:39Z",
      "native_id": "hal-05760108",
      "source": "hal",
      "url": "https://hal.science/hal-05760108v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration",
  "title_text": "Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:39Z",
  "url": "https://research.draconitic.com/paper/6b5ysf1n3nmcg",
  "venue": "HAL",
  "versions": []
}