Equivariant Neural Diffusion for Molecule Generation
Existing 3D molecular diffusion models struggle to simultaneously satisfy SE(3) equivariance and high generation quality. To address this, we propose the first equivariant neural diffusion model specifically designed for 3D molecular generation. Our core innovation is a learnable, time- and data-dependent equivariant forward process—enabling strict SE(3) equivariance (i.e., invariance under rigid rotations and translations) in diffusion modeling for the first time, thereby overcoming the limitations of conventional fixed noise schedules. The model integrates an SE(3)-equivariant neural network backbone with a coordinate-aware denoising architecture, preserving theoretical equivariance while substantially enhancing representational capacity and generative flexibility. Extensive experiments on standard molecular generation benchmarks demonstrate state-of-the-art or best-in-class performance in both unconditional and conditional generation tasks. Moreover, the generated molecules exhibit significantly improved validity, chemical feasibility, and structural fidelity.