Kinetic Langevin Diffusion for Crystalline Materials Generation
Submission Track: Full Paper
Submission Category: AI-Guided Design
Keywords: diffusion models, 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 Models (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 consistent with the periodic translation symmetry of
the true data distribution. We evaluate KLDM on both Crystal Structure Predic-
tion (CSP) and De-novo Generation (DNG) tasks, demonstrating its competitive
performance with current state-of-the-art models.
Submission Number: 21
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