Deep generative models have made remarkable strides in crystal design. Because crystalline structures inherently possess space‑group symmetries, recent studies have tried to embed these symmetries directly into generative models to explore novel symmetry templates more efficiently. However, adding explicit symmetry templates dramatically increases the combinatorial complexity of stoichiometric relationships between atomic species and crystallographic sites, and creates a fundamental tension between exploring discrete crystallographic templates and realizing them as continuous three‑dimensional structures. To tackle these issues, we introduce CrystalAR, a unified autoregressive framework that models Wyckoff symmetry templates and full crystal structures within a single generation sequence. CrystalAR reformulates continuous coordinate generation as a hierarchy of discrete spatial‑localization decisions conditioned on symmetry, autoregressively refining the positions of all symmetry‑inequivalent sites across multiple resolution levels while jointly modeling their spatial configuration at each level. This discrete hierarchical formulation enables constraint‑aware search over both crystallographic templates and their geometric realizations, preserving strong template‑generation capability while achieving competitive de novo generation performance and template‑free crystal structure prediction (CSP) accuracy. Experiments demonstrate that retaining symmetry‑template generation does not sacrifice overall quality; even without relying on templates extracted from prior data, CrystalAR attains competitive CSP results, offering a promising alternative paradigm for symmetry‑preserving crystal generation.
Review