Deep learning-based generative models hold significant promise for exploring the configuration space of crystalline materials, though their application remains in its early stages. In this study, we present CrystalFlow, a flow-based generative model designed to address the unique challenges of this domain. By combining Continuous Normalizing Flows and Conditional Flow Matching with a graph-based equivariant neural network and symmetry-aware data representations, CrystalFlow efficiently models lattice parameters, atomic coordinates, and atom types. This architecture enables data-efficient learning and the generation of high-quality crystal structures. Our results indicate that CrystalFlow achieves performance comparable to state-of-the-art models on established benchmarks while exhibiting versatile conditional generation capabilities (e.g., predicting structures under specific pressures or material properties), and is approximately an order of magnitude more efficient than diffusion-based models in terms of integration steps. Deep learning generative models hold significant promise for exploring the configuration space of crystalline materials. Here, the authors present CrystalFlow, a flow-based generative model for crystal structure prediction and materials discovery.
Luo et al. (Mon,) studied this question.