  Denoising diffusion probabilistic models (DDPMs) have pioneered new
state-of-the-art results in disciplines such as computer vision and
computational biology for diverse tasks ranging from text-guided image
generation to structure-guided protein design. Along this latter line of
research, methods have recently been proposed for generating 3D molecules using
equivariant graph neural networks (GNNs) within a DDPM framework. However, such
methods are unable to learn important geometric properties of 3D molecules, as
they adopt molecule-agnostic and non-geometric GNNs as their 3D graph denoising
networks, which notably hinders their ability to generate valid large 3D
molecules. In this work, we address these gaps by introducing the
Geometry-Complete Diffusion Model (GCDM) for 3D molecule generation, which
outperforms existing 3D molecular diffusion models by significant margins
across conditional and unconditional settings for the QM9 dataset and the
larger GEOM-Drugs dataset, respectively, and generates more novel and unique
unconditional 3D molecules for the QM9 dataset compared to previous methods.
Importantly, we demonstrate that the geometry-complete denoising process of
GCDM learned for 3D molecule generation enables the model to generate a
significant proportion of valid and energetically-stable large molecules at the
scale of GEOM-Drugs, whereas previous methods fail to do so with the features
they learn. Additionally, we show that extensions of GCDM can not only
effectively design 3D molecules for specific protein pockets but also that
GCDM's geometric features can be repurposed to consistently optimize the
geometry and chemical composition of existing 3D molecules for molecular
stability and property specificity, demonstrating new versatility of molecular
diffusion models. Our source code and data are freely available at
https://github.com/BioinfoMachineLearning/Bio-Diffusion.
