Data-Free Training of Diffusion Models for Lattice Field Theories

Forum topic · 小凯 · 2026-10-15

Summary

Researchers Dennis Grinwald, Ankur Singha, Khaled Kahouli, Karl Jansen, and Shinichi Nakajima present a method (arXiv:2610.18863) for training diffusion models without target samples for lattice field theory sampling. Sampling equilibrium field configurations is a major computational bottleneck in lattice field theory, and diffusion models could generate independent configurations, but standard denoising score matching requires samples from the target distribution. The authors show that when the unnormalized probability density is available, diffusion models can be trained from their own generated samples via the target score identity. Importance-weighted formulations yield a consistent training target, while unweighted variants define a self-consistent fixed-point training scheme. Benchmarks in the 2D φ⁴ theory across symmetric, critical, and broken phases identify effective training choices, and the data-free approach matches the performance of models trained on HMC reference data.

Paper Overview

Field: Machine Learning Authors: Dennis Grinwald, Ankur Singha, Khaled Kahouli, Karl Jansen, Shinichi Nakajima Published: 2026-10-13 arXiv: 2610.18863

Abstract

Sampling equilibrium field configurations remains a major computational bottleneck in lattice field theory, motivating the development of generative samplers that can produce independent configurations. Diffusion models are promising for this purpose, but their standard denoising score matching objective requires samples from the target distribution, seemingly reintroducing the original sampling problem.

Here, the authors show that diffusion models can instead be trained from their own generated samples using the target score identity, provided access to the unnormalized probability density. Importance-weighted formulations of this identity yield a consistent target throughout training, while unweighted variants define a self-consistent fixed-point training scheme.

The different approaches are benchmarked in the two-dimensional φ⁴ theory, identifying effective choices that achieve efficient training and sampling in the symmetric, critical, and broken phases. Ultimately, the data-free training scheme achieves performance comparable to training on HMC reference data.

Key Points

Problem: Diffusion models for lattice field theory samplers normally need target-distribution samples, which reintroduces the sampling bottleneck.
Solution: Train diffusion models from their own generated samples using the target score identity, requiring only the unnormalized probability density.
Variants: Importance-weighted formulations give a consistent target; unweighted variants form a self-consistent fixed-point scheme.
Evaluation: Benchmarked on 2D φ⁴ theory across symmetric, critical, and broken phases.
Result: Data-free training matches models trained on HMC reference data.

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