{
  "abstract": "We introduce sticky jump diffusions (SJDs), continuous-time Markov processes on $\\mathbb{R}^d$ whose discrete anchors are token embeddings. In forward time, anchors release their mass at a hazard rate and the released mass diffuses in the continuous ambient space; time reversal couples a score-driven SDE with a sticky jump kernel whose rate and destination are fixed by flux balance with the forward law. We estimate the score and the per-anchor reverse hazards from a single denoising classifier via denoising hazard matching, the hazard analogue of denoising score matching, with simulation-free cross-entropy training. SJD recovers masked diffusion, continuous diffusion, and hybrid diffusion as limits. Its reversal explains features that each family treats as given: the mask of masked diffusion carries no evidence about the source token because the unsticking kernel of every anchor collapses to the same absorbing point; the terminal projection of continuous diffusion is required due to the absence of atoms in its forward marginal, without which flux balance yields no reverse jumps; and the update rules of hybrid diffusion (commit rate, destination, and drift) all follow from flux balance rather than from separate design. Beyond these limits, the unsticking kernel becomes a design space: a cross-position blending corrupts each position toward a blend of its neighbors' clean values or embeddings, turning dependency structure such as spatial locality or a constraint graph into an inductive bias of the corruption itself, and improves over the identity-kernel hybrid on CIFAR-10, Text8, and Sudoku.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.10951",
  "author_total": 5,
  "authors": [
    {
      "name": "Pascal Jutras-Dubé"
    },
    {
      "name": "Patrick Pynadath"
    },
    {
      "name": "Jeremy Lu"
    },
    {
      "name": "Yuan Gao"
    },
    {
      "name": "Ruqi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekcqqfwnnf96w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.10951",
  "fulltext_url": null,
  "id": "ekcqqfwnnf96w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.10951",
  "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": "W7168295487",
  "pdf_url": "https://arxiv.org/pdf/2607.10951",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekcqqfwnnf96w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:41Z",
      "native_id": "2607.10951",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.10951"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion",
  "title_text": "Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/ekcqqfwnnf96w",
  "venue": "arXiv",
  "versions": []
}