  We introduce a new framework for molecular graph generation with 3D molecular
generative models. Our Synthetic Coordinate Embedding (SyCo) framework maps
molecular graphs to Euclidean point clouds via synthetic conformer 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 molecular generative models. This approach simplifies the graph
generation problem - without relying on molecular fragments nor autoregressive
decoding - into a point cloud generation problem followed by node and edge
classification tasks. 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 30% on ZINC250K and 16% on the
large-scale GuacaMol dataset while improving conditional generation by up to
3.9 times.
