Kinetic Langevin Diffusion for Crystalline Materials Generation

François R J Cornet, Federico Bergamin, Arghya Bhowmik, Juan Maria Garcia-Lastra, Jes Frellsen, Mikkel N. Schmidt
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:11215-11244, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-cornet25a, title = {Kinetic {L}angevin Diffusion for Crystalline Materials Generation}, author = {Cornet, Fran\c{c}ois R J and Bergamin, Federico and Bhowmik, Arghya and Garcia-Lastra, Juan Maria and Frellsen, Jes and Schmidt, Mikkel N.}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {11215--11244}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/cornet25a/cornet25a.pdf}, url = {https://proceedings.mlr.press/v267/cornet25a.html}, 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.} }
Endnote
%0 Conference Paper %T Kinetic Langevin Diffusion for Crystalline Materials Generation %A François R J Cornet %A Federico Bergamin %A Arghya Bhowmik %A Juan Maria Garcia-Lastra %A Jes Frellsen %A Mikkel N. Schmidt %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-cornet25a %I PMLR %P 11215--11244 %U https://proceedings.mlr.press/v267/cornet25a.html %V 267 %X 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.
APA
Cornet, F.R.J., Bergamin, F., Bhowmik, A., Garcia-Lastra, J.M., Frellsen, J. & Schmidt, M.N.. (2025). Kinetic Langevin Diffusion for Crystalline Materials Generation. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:11215-11244 Available from https://proceedings.mlr.press/v267/cornet25a.html.

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