{
  "abstract": "We discuss diffusion-model paths interpolating between a target distribution known only through p patterns and a reference distribution that can be sampled. These interpolating paths can be constructed symmetrically or else in forward direction (often referred to as a \"noising\") from the target patterns to the reference distribution or in backward direction (as a \"denoising\") from the reference distribution to the patterns. For backward paths with identical diffusion noise, we consider the path convergence in number of patterns p towards the path for infinitely many patterns. In a one-dimensional test case, we show that this convergence is on a scale 1/sqrt(p), but with infinite mean square deviation. We demonstrate that the path convergence allows for extrapolation towards the p=infinity path which samples the target distribution. We provide a proof-of-concept extrapolation algorithm and propose the convergence and extrapolation of paths as a possible strategy for density estimation and generalization. We illustrate all our algorithms through pseudo-codes and provide Python implementations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: EPL 156 (2026) 61007",
  "arxiv": "2606.12161",
  "author_total": 3,
  "authors": [
    {
      "name": "Roi Holtzman"
    },
    {
      "name": "Roman Beauvallet"
    },
    {
      "name": "Werner Krauth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b99eghhe8q9ck.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.12161",
  "fulltext_url": null,
  "id": "b99eghhe8q9ck",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.12161",
  "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",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.12161",
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b99eghhe8q9ck.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:58Z",
      "native_id": "2606.12161",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.12161"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Path convergence in diffusion models",
  "title_text": "Path convergence in diffusion models",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:17Z",
  "url": "https://research.draconitic.com/paper/b99eghhe8q9ck",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1209/0295-5075/aeac3c",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}