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This paper tackles a practical bottleneck: training diffusion models without the Monte Carlo samples they usually need, by learning from their own outputs via a target score identity and an unnormalized density. The reported result is that this data-free approach roughly matches training on HMC reference data for 2D φ⁴ theory across several phases. For ML readers, the key questions are the stability of the self-consistent training schemes and whether the gains hold for larger lattices and other field theories.
Data Free Training of Diffusion Models for Lattice Field Theories
arXiv:2610.18863v1 Announce Type: cross 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, we 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. We benchmark the different approaches in two-dimensional \(\phi^4\) theory and identify effective choices that enable efficient training and sampling across the symmetric, critical, and broken phases. Ultimately, our data-free training approach achieves comparable performance to training on HMC reference data.
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, we 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. We benchmark the different approaches in two-dimensional \(\phi^4\) theory and identify effective choices that enable efficient training and sampling across the symmetric, critical, and broken phases. Ultimately, our data-free training approach achieves comparable performance to training on HMC reference data.
High Energy Physics - Lattice (hep-lat); Machine Learning (cs.LG)
arXiv:2610.18863 [hep-lat]
(or arXiv:2610.18863v1 [hep-lat] for this version)
https://doi.org/10.48550/arXiv.2610.18863 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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