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.
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