Representation-space diffusion models for generating periodic materials

Abstract: Generative models hold the promise of significantly expediting the materials design process when compared to traditional human-guided or rule-based methodologies. However, effectively generating high-quality periodic structures of materials on limited but diverse datasets remains an ongoing challenge. Here we propose a novel approach for periodic structure generation which fully respect the intrinsic symmetries, periodicity, and invariances of the structure space. Namely, we utilize differentiable, physics-based, structural descriptors which can describe periodic systems and satisfy the necessary invariances, in conjunction with a denoising diffusion model which generates new materials within this descriptor or representation space. Reconstruction is then performed on these representations using gradient-based optimization to recover the corresponding Cartesian positions of the crystal structure. This approach differs significantly from current methods by generating materials in the representation space, rather than in the Cartesian space, which is made possible using an efficient reconstruction algorithm. Consequently, known issues with respecting periodic boundaries and translational and rotational invariances during generation can be avoided, and the model training process can be greatly simplified. We show this approach is able to provide competitive performance on established benchmarks compared to current state-of-the-art methods.