免数据训练扩散模型，用于格点场理论采样
Data Free Training of Diffusion Models for Lattice Field Theories
不用 HMC 先采样就能训练扩散模型，靠自身生成的样本自举，在二维 φ⁴ 理论上效果追平有数据训练。
格点场理论中采样平衡场组态是主要计算瓶颈，而扩散模型的标准去噪分数匹配目标需要先从目标分布采样，等于把原问题带了回来。论文利用目标分数恒等式，只需未归一化概率密度，就能让扩散模型用自身生成的样本完成训练，其中重要性加权形式保证训练目标一致，未加权形式构成自洽的不动点训练方案。方法在二维 φ⁴ 理论的对称相、临界相和破缺相做了基准测试，确定了高效训练与采样的有效配置。最终这种免数据训练的性能与基于 HMC 参考数据的训练相当。
Data Free Training of Diffusion Models for Lattice Field Theories
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 \(φ^4\) 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.
