Lift Your Molecules: Molecular Graph Generation in Latent Euclidean Space

We introduce a new framework for 2D molecular graph generation using 3D molecule generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps 2D molecular graphs to 3D Euclidean point clouds via synthetic coordinates and learns the inverse map using an E($n$)-Equivariant Graph Neural Network (EGNN). The induced point cloud-structured latent space is well-suited to apply existing 3D molecule generative models. This approach simplifies the graph generation problem into a point cloud generation problem followed by node and edge classification tasks, without relying on molecular fragments nor autoregressive decoding. Further, we propose a novel similarity-constrained optimization scheme for 3D diffusion models based on inpainting and guidance. As a concrete implementation of our framework, we develop EDM-SyCo based on the E(3) Equivariant Diffusion Model (EDM). EDM-SyCo achieves state-of-the-art performance in distribution learning of molecular graphs, outperforming the best non-autoregressive methods by more than 26\% on ZINC250K and 16\% on the GuacaMol dataset while improving conditional generation by up to 3.9 times.