Lattice Configuration Generation with a Self-Learning Diffusion Model

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.

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BibTeX RIS

BibTeX

@misc{tomiya2026lattice,
  title = {{Lattice Configuration Generation with a Self-Learning Diffusion Model}},
  author = {Akio Tomiya},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.12587},
  eprint = {2607.12587},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.12587},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Lattice Configuration Generation with a Self-Learning Diffusion Model
AU  - Akio Tomiya
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2607.12587
UR  - https://arxiv.org/abs/2607.12587
AB  - 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.
ER  -

Abstract

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