Diffusion-based generative models in SE(3)-invariant space have demonstrated promising performance in molecular conformation generation, but typically require solving stochastic differential equations (SDEs) with thousands of update steps. Till now, it remains unclear how to effectively accelerate this procedure explicitly in SE(3)-invariant space, which greatly hinders its wide application in the real world. In this paper, we systematically study the diffusion mechanism in SE(3)-invariant space via the lens of approximate errors induced by existing methods. Thereby, we develop more precise approximate in SE(3) in the context of projected differential equations. Theoretical analysis is further provided as well as empirical proof relating hyper-parameters with such errors. Altogether, we propose a novel acceleration scheme for generating molecular conformations in SE(3)-invariant space. Experimentally, our scheme can generate high-quality conformations with 50x--100x speedup compared to existing methods.

翻译：在SE(3)不变空间中基于扩散的生成模型已在分子构象生成中展现出良好的性能，但通常需要求解包含数千个更新步的随机微分方程(SDEs)。迄今，如何在SE(3)不变空间中有效加速这一过程仍不明确，这极大地阻碍了其在实际中的广泛应用。本文通过现有方法引入的近似误差视角，系统研究了SE(3)不变空间中的扩散机制。在此基础上，我们在投影微分方程框架下发展了更精确的SE(3)近似方法。进一步提供了超参数与这类误差之间关系的理论分析及实证证据。综合而言，我们提出了一种在SE(3)不变空间中生成分子构象的新型加速方案。实验表明，与现有方法相比，该方案能够以50倍至100倍的速度提升生成高质量构象。