[论文] Data Free Training of Diffusion Models for Lattice Field Theories

论文概要

研究领域: ML
作者: Dennis Grinwald, Ankur Singha, Khaled Kahouli, Karl Jansen, Shinichi Nakajima
发布时间: 2026-10-13
arXiv: 2610.18863

中文摘要

采样平衡场构型仍然是格点场论中的主要计算瓶颈，这促使人们开发能够生成独立构型的生成式采样器。扩散模型在这方面很有前景，但其标准的去噪分数匹配目标需要来自目标分布的样本，这似乎重新引入了原来的采样问题。本文证明，只要可以访问未归一化的概率密度，扩散模型就可以使用目标分数恒等式从自身的生成样本中进行训练。该恒等式的重要性加权形式在训练全程产生一致的目标，而非加权变体定义了一种自洽的不动点训练方案。我们在二维 φ⁴ 理论中对不同方法进行了基准测试，确定了在对称相、临界相和破缺相中都能实现高效训练和采样的有效选择。最终，我们的无数据训练方案达到了与在 HMC 参考数据上训练相当的性能。

原文摘要

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 approa...

自动采集于 2026-10-15

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