In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular systems. However, while classical diffusion sampling usually recovers the training distribution, the corresponding energy-based interpretation of the learned score is often inconsistent with this distribution, even for low-dimensional toy systems. We trace this inconsistency to inaccuracies of the learned score at very small diffusion timesteps, where the model must capture the correct evolution of the data distribution. In this regime, diffusion models fail to satisfy the Fokker-Planck equation, which governs the evolution of the score. We interpret this deviation as one source of the observed inconsistencies and propose an energy-based diffusion model with a Fokker-Planck-derived regularization term to enforce consistency. We demonstrate our approach by sampling and simulating multiple biomolecular systems, including fast-folding proteins, and by introducing a state-of-the-art transferable Boltzmann emulator for dipeptides that supports simulation and achieves improved consistency and efficient sampling. Our code, model weights, and self-contained JAX and PyTorch notebooks are available at https://github.com/noegroup/ScoreMD.

翻译：近年来，在平衡态分子分布上训练的扩散模型已被证明对生物分子采样具有良好效果。除直接采样外，此类模型的评分函数还可用于推导分子系统所受作用力。然而，尽管经典扩散采样通常能复现训练分布，但所学评分函数对应的基于能量的解释常与该分布不一致，即使在低维玩具系统中亦是如此。我们将这种不一致性归因于所学评分函数在极小扩散时间步长下的不准确性——此时模型必须捕捉数据分布的正确演化。在此区域，扩散模型未能满足支配评分演化的福克-普朗克方程。我们将此偏差解释为观测不一致性的来源之一，并提出一种基于能量的扩散模型，其通过福克-普朗克导出的正则化项来保证一致性。我们通过对多个生物分子系统（包括快速折叠蛋白质）进行采样与模拟，并构建支持模拟的二肽可迁移玻尔兹曼模拟器（该模拟器实现了改进的一致性与高效采样），验证了所提方法的有效性。我们的代码、模型权重及独立运行的JAX与PyTorch笔记本可在https://github.com/noegroup/ScoreMD获取。