用对称性约束生成2D材料，提升稳定结构发现效率

Generative model for 2D materials has shown significant promise in accelerating the material discovery process. The stability and performance of these materials are strongly influenced by their underlying symmetry. However, existing generative models for 2D materials often neglect symmetry constraints, which limits both the diversity and quality of the generated structures. Here, we introduce a symmetry-constrained diffusion model (SCDM) that integrates space group symmetry into the generative process. By incorporating Wyckoff positions, the model ensures adherence to symmetry principles, leading to the generation of 2,000 candidate structures. DFT calculations were conducted to evaluate the convex hull energies of these structures after structural relaxation. From the generated samples, 843 materials that met the energy stability criteria (Ehull < 0.6 eV/atom) were identified. Among these, six candidates were selected for further stability analysis, including phonon band structure evaluations and electronic properties investigations, all of which exhibited phonon spectrum stability. To benchmark the performance of SCDM, a symmetry-unconstrained diffusion model was also evaluated via crystal structure prediction model. The results highlight that incorporating symmetry constraints enhances the effectiveness of generated 2D materials, making a contribution to the discovery of 2D materials through generative modeling.