Inverse molecular design is critical in material science and drug discovery, where the generated molecules should satisfy certain desirable properties. In this paper, we propose equivariant energy-guided stochastic differential equations (EEGSDE), a flexible framework for controllable 3D molecule generation under the guidance of an energy function in diffusion models. Formally, we show that EEGSDE naturally exploits the geometric symmetry in 3D molecular conformation, as long as the energy function is invariant to orthogonal transformations. Empirically, under the guidance of designed energy functions, EEGSDE significantly improves the baseline on QM9, in inverse molecular design targeted to quantum properties and molecular structures. Furthermore, EEGSDE is able to generate molecules with multiple target properties by combining the corresponding energy functions linearly.

翻译：逆向分子设计在材料科学和药物发现中至关重要，其生成的分子应满足特定的目标属性。本文提出等变能量引导随机微分方程（EEGSDE），这是一个在扩散模型中通过能量函数引导实现可控三维分子生成的灵活框架。在形式上，我们证明只要能量函数对正交变换具有不变性，EEGSDE就能自然地利用三维分子构象的几何对称性。在实验上，通过设计能量函数的引导，EEGSDE在面向量子属性和分子结构的逆向分子设计任务中，显著提升了QM9基准数据集上的基线表现。此外，通过线性组合对应的能量函数，EEGSDE能够生成具有多个目标属性的分子。