Diffusion Models for 3D Molecular and Crystal Structure Generation: Advancing Materials Discovery through Equivariance, Multi-Property Design, and Synthesizability

Diffusion models are rapidly transforming the field of computational materials design. This review examines their application to 3D molecular and crystal structure generation, focusing on key challenges and recent advances. We analyze how equivariance principles and manifold learning contribute to generating physically realistic structures. We discuss innovations in symmetry-preserving crystal generation and multi-property directed design. A critical assessment is provided of methods to improve sampling efficiency, incorporate force field guidance, and utilize joint 2D-3D representations. Furthermore, we emphasize the importance of integrating synthesizability considerations and reaction knowledge to accelerate the materials discovery process.