SymADiT: Symmetry-Aware Crystal Generation with Latent Flow Matching
Abstract
Tackling the task of crystal generation, we aim to enhance the previously proposed, symmetry-agnostic, All-atom Diffusion Transformer (ADiT) by introducing SymADiT, a symmetry-aware variant. To do so, we use a representation of crystals based on Wyckoff positions. We follow ADiT and perform generative modelling in latent space, adapted to our symmetry-aware representation. By forcing the output of the generative model to adhere to the symmetry restrictions imposed by the generated crystal's space group and each atom's Wyckoff position, the generated crystals exhibit more realistic symmetry properties. We benchmark our method against both symmetry-aware and symmetry-agnostic models for crystal generation and show competitive performance, generating stable, symmetric, and physically plausible crystals with only an off-the-shelf Transformer architecture. Our code is available at https://github.com/Karmush21/SymADiT.
Related
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- Symmetry-aware super-resolution of crystal orientation maps via invariant latent-space learning
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- GEODE: Symmetry-Preserving Cartesian Diffusion for Crystal Generation
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BibTeX
@misc{karmush2026symadit,
title = {{SymADiT: Symmetry-Aware Crystal Generation with Latent Flow Matching}},
author = {Anmar Karmush and Cedric Mathieu Brandenburg and Soheil Ershadrad and Johanna Rosen and Michael Felsberg and Filip Ekström Kelvinius},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.10115},
eprint = {2605.10115},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10115},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SymADiT: Symmetry-Aware Crystal Generation with Latent Flow Matching
AU - Anmar Karmush
AU - Cedric Mathieu Brandenburg
AU - Soheil Ershadrad
AU - Johanna Rosen
AU - Michael Felsberg
AU - Filip Ekström Kelvinius
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2605.10115
UR - https://arxiv.org/abs/2605.10115
AB - Tackling the task of crystal generation, we aim to enhance the previously proposed, symmetry-agnostic, All-atom Diffusion Transformer (ADiT) by introducing SymADiT, a symmetry-aware variant. To do so, we use a representation of crystals based on Wyckoff positions. We follow ADiT and perform generative modelling in latent space, adapted to our symmetry-aware representation. By forcing the output of the generative model to adhere to the symmetry restrictions imposed by the generated crystal's space group and each atom's Wyckoff position, the generated crystals exhibit more realistic symmetry properties. We benchmark our method against both symmetry-aware and symmetry-agnostic models for crystal generation and show competitive performance, generating stable, symmetric, and physically plausible crystals with only an off-the-shelf Transformer architecture. Our code is available at https://github.com/Karmush21/SymADiT.
ER -