arXiv:2608.07401v2 Announce Type: replace-cross Abstract: The search for new crystalline materials spans an enormous compositional and structural space. Generating candidates in this space requires modeling the relationships between elemental composition, crystallographic symmetry, and crystal geometry. The space group specifies the crystal's symmetry and determines the admissible Wyckoff positions and geometric degrees of freedom; fixing it in advance prevents this global symmetry choice from being revised using information from evolving Wyckoff occupations and elemental composition. We introduce DynaCrys, the first framework for complete crystal generation in which the space group co-evolves with Wyckoff occupations and elements. We develop physics-informed space-group diffusion that explicitly incorporates crystallographic group-subgroup relations, and a legality-constrained stochastic decoder that jointly samples compatible space groups, Wyckoff occupations, and elements, followed by symmetry-constrained geometry generation. In large-scale evaluations on standard benchmarks, DynaCrys achieves state-of-the-art performance in symmetry-aware crystal generation while supporting fast sampling.