  Discovering crystal structures with specific chemical properties has become
an increasingly important focus in material science. However, current models
are limited in their ability to generate new crystal lattices, as they only
consider atomic positions or chemical composition. To address this issue, we
propose a probabilistic diffusion model that utilizes a geometrically
equivariant GNN to consider atomic positions and crystal lattices jointly. To
evaluate the effectiveness of our model, we introduce a new generation metric
inspired by Frechet Inception Distance, but based on GNN energy prediction
rather than InceptionV3 used in computer vision. In addition to commonly used
metrics like validity, which assesses the plausibility of a structure, this new
metric offers a more comprehensive evaluation of our model's capabilities. Our
experiments on existing benchmarks show the significance of our diffusion
model. We also show that our method can effectively learn meaningful
representations.
