Kinetic Langevin Diffusion for Crystalline Materials Generation

TL;DR

This paper introduces Kinetic Langevin Diffusion for Materials (KLDM), a novel diffusion model that effectively generates crystalline materials by modeling atomic coordinates on a hypertorus with symmetry considerations.

Contribution

The work generalizes the Trivialized Diffusion Model to account for crystal symmetries, coupling coordinates with velocities to perform diffusion on a hypertorus effectively.

Findings

Competitive performance on crystal structure prediction

Effective modeling of fractional coordinates on a hypertorus

Advances in generative modeling for crystalline materials

Abstract

Generative modeling of crystalline materials using diffusion models presents a series of challenges: the data distribution is characterized by inherent symmetries and involves multiple modalities, with some defined on specific manifolds. Notably, the treatment of fractional coordinates representing atomic positions in the unit cell requires careful consideration, as they lie on a hypertorus. In this work, we introduce Kinetic Langevin Diffusion for Materials (KLDM), a novel diffusion model for crystalline materials generation, where the key innovation resides in the modeling of the coordinates. Instead of resorting to Riemannian diffusion on the hypertorus directly, we generalize Trivialized Diffusion Model (TDM) to account for the symmetries inherent to crystals. By coupling coordinates with auxiliary Euclidean variables representing velocities, the diffusion process is now offset to a flat space. This allows us to effectively perform diffusion on the hypertorus while providing a training objective that accounts for the periodic translation symmetry of the true data distribution. We evaluate KLDM on both Crystal Structure Prediction (CSP) and De-novo Generation (DNG) tasks, demonstrating its competitive performance with current state-of-the-art models.