Symmetry-Aware Flow Matching for End-to-end Molecular Crystal Generation

Wendi Cai${}^{ \dagger }$ and Fanyang Mo${}^{ * }$

${}^{1}$ School of AI for Science, Peking University Shenzhen Graduate School, Shenzhen 518055, China; ${}^{2}$ School of Advanced Materials, Peking University Shenzhen Graduate School, Shenzhen 518055, China; ${}^{3}$ Guangdong Provincial Key Laboratory of Nano-Micro Materials Research, Peking University Shenzhen Graduate School, Shenzhen 518055, China; ${}^{4}$ State Key Laboratory of Advanced Waterproof Materials, School of Materials Science and Engineering, Peking University, Beijing 100871, China. ${}^{ \dagger }$ Work completed during an internship at ByteDance. ${}^{ * }$ Corresponding author.

Cite This: arXiv: 2609.34690 (2026). https://arxiv.org/abs/2609.34690. Submitted September 28, 2026.

ABSTRACT: Molecular crystal packing shapes properties from drug bioavailability to charge transport, yet generating realistic structures requires coordinating molecular flexibility, intermolecular interactions and symmetry. Here we introduce SALA, a flow-matching model built on state–context separation: it evolves only asymmetric-unit (ASU) atomic coordinates and symmetry-compatible lattice parameters while predicting their updates from the full periodic environment. Conditioned on molecular graphs and a space group, SALA generates molecular conformation, lattice geometry and packing end to end while preserving the specified symmetry. Across 799 held-out crystals spanning four chemical classes and all seven crystal systems, SALA achieves a 72.0% hit rate from 50 candidates per target, compared with 8.1% for an atomistic full-cell generative baseline. Mean best-candidate packing root-mean-square deviation decreases from 4.48 to 1.70 Å, with the advantage widening as system size and symmetry multiplicity increase. SALA thus enables end-to-end generation of complex, symmetry-constrained molecular crystals, with potential applications in CSP, structure-based pharmaceutical polymorph design and organic molecular materials discovery.

Note: This is an arXiv preprint; the full bilingual text is to be added. Preprint: arXiv: 2609.34690.