Enhancing materials discovery with valence-constrained design in generative modeling.

Diffusion-based deep generative models have emerged as powerful tools for inverse materials design. Yet many existing approaches overlook essential chemical constraints, such as oxidation-state balance, which can lead to chemically invalid structures. Here we introduce 'crystal generator with valence-constrained design' (CrysVCD), a modular framework that integrates chemical rules directly into the generative process. CrysVCD first uses a transformer-based elemental language model to generate valence-balanced compositions, followed by a diffusion model to generate crystal structures. The valence constraint enables orders-of-magnitude more efficient chemical valence checking compared with pure data-driven approaches with post-screening. When fine-tuned on stability metrics, CrysVCD achieves 85% metastability (Ehull < 0.1 eV per atom) and 68% phonon stability. Moreover, CrysVCD supports conditional generation of functional materials, enabling discovery of candidates such as high thermal conductivity semiconductors and high dielectric constant (high-κ) materials. Designed as a general-purpose plugin, CrysVCD can be integrated into diverse generative pipelines to promote chemical validity, offering a reliable, scientifically grounded path for materials discovery.