ICML 2025

Kinetic Langevin Diffusion for Crystalline Materials Generation
Franc¸ois Cornet * 1 Federico Bergamin * 1 2
Arghya Bhowmik 1 Juan Maria Garcia Lastra 1 Jes Frellsen 1 2 Mikkel N. Schmidt 1 2
Abstract
Generative modeling of crystalline materials us-
ing diffusion models presents a series of chal-
lenges: the data distribution is characterized by in-
herent symmetries and involves multiple modali-
ties, with some defined on specific manifolds. No-
tably, the treatment of fractional coordinates rep-
resenting atomic positions in the unit cell requires
careful consideration, as they lie on a hypertorus.
In this work, we introduce Kinetic Langevin Dif-
fusion 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 effec-
tively 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 Genera-
tion (DNG) tasks, demonstrating its competitive
performance with current state-of-the-art models.
1. Introduction
The discovery of novel compounds with desired properties is
critical to several scientific fields, such as molecular discov-
ery (Bilodeau et al., 2022) and materials design (Merchant
et al., 2023; Zeni et al., 2025). In the case of crystalline
materials, the search space is vast, but only a fraction of it is
physically plausible. The main challenges are to efficiently
*Equal contribution
1Technical University of Denmark, Kon-
gens Lyngby, Denmark 2Pioneer Center for Artificial Intellig...