  The discovery of new functional and stable materials is a big challenge due
to its complexity. This work aims at the generation of new crystal structures
with desired properties, such as chemical stability and specified chemical
composition, by using machine learning generative models. Compared to the
generation of molecules, crystal structures pose new difficulties arising from
the periodic nature of the crystal and from the specific symmetry constraints
related to the space group. In this work, score-based probabilistic models
based on annealed Langevin dynamics, which have shown excellent performance in
various applications, are adapted to the task of crystal generation. The
novelty of the presented approach resides in the fact that the lattice of the
crystal cell is not fixed. During the training of the model, the lattice is
learned from the available data, whereas during the sampling of a new chemical
structure, two denoising processes are used in parallel to generate the lattice
along the generation of the atomic positions. A multigraph crystal
representation is introduced that respects symmetry constraints, yielding
computational advantages and a better quality of the sampled structures. We
show that our model is capable of generating new candidate structures in any
chosen chemical system and crystal group without any additional training. To
illustrate the functionality of the proposed method, a comparison of our model
to other recent generative models, based on descriptor-based metrics, is
provided.
