  Designing new molecules is essential for drug discovery and material science.
Recently, deep generative models that aim to model molecule distribution have
made promising progress in narrowing down the chemical research space and
generating high-fidelity molecules. However, current generative models only
focus on modeling either 2D bonding graphs or 3D geometries, which are two
complementary descriptors for molecules. The lack of ability to jointly model
both limits the improvement of generation quality and further downstream
applications. In this paper, we propose a new joint 2D and 3D diffusion model
(JODO) that generates complete molecules with atom types, formal charges, bond
information, and 3D coordinates. To capture the correlation between molecular
graphs and geometries in the diffusion process, we develop a Diffusion Graph
Transformer to parameterize the data prediction model that recovers the
original data from noisy data. The Diffusion Graph Transformer interacts node
and edge representations based on our relational attention mechanism, while
simultaneously propagating and updating scalar features and geometric vectors.
Our model can also be extended for inverse molecular design targeting single or
multiple quantum properties. In our comprehensive evaluation pipeline for
unconditional joint generation, the results of the experiment show that JODO
remarkably outperforms the baselines on the QM9 and GEOM-Drugs datasets.
Furthermore, our model excels in few-step fast sampling, as well as in inverse
molecule design and molecular graph generation. Our code is provided in
https://github.com/GRAPH-0/JODO.
