{
  "abstract": "We show that a diffusion sampler for lattice-field configurations can be self-trained without preparing target-ensemble training configurations using an external Monte Carlo calculation. Starting from exactly sampled configurations at $β=0$, we use action-difference weights to train the score at the next coupling. Proposals from a fixed model are Metropolis-Hastings corrected at every noise level, and the resulting chain supplies training configurations for the next stage. This procedure defines the self-learning diffusion sampler SLDiffusion. In the two-dimensional compact XY model, self-training proceeds from $β=0.30$ to $0.50$ at $L=4$ and extends to $L=6,8,12$ at $β=0.5$. The energy and vortex densities agree with independent Hybrid Monte Carlo calculations within $1.6$ combined standard errors. Their integrated autocorrelation times, measured in stored updates, remain below two at all volumes studied. These results demonstrate a diffusion sampler whose training can be initialized and continued without external target-coupling ensembles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.12587",
  "author_total": 1,
  "authors": [
    {
      "name": "Akio Tomiya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2j1wdfy8rx4pk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.12587",
  "fulltext_url": null,
  "id": "2j1wdfy8rx4pk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.12587",
  "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.str-el"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7168403525",
  "pdf_url": "https://arxiv.org/pdf/2607.12587",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2j1wdfy8rx4pk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2607.12587",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.12587"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    }
  ],
  "title": "Lattice Configuration Generation with a Self-Learning Diffusion Model",
  "title_text": "Lattice Configuration Generation with a Self-Learning Diffusion Model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/2j1wdfy8rx4pk",
  "venue": "arXiv",
  "versions": []
}