CrystalDLM: Feedback Learning of Periodic Diffusion Language Models for Crystal Generation

Crystal generation requires compatible periodic arrangements of atoms, yet geometric validity alone does not guarantee physical quality. We introduce CrystalDLM, a framework built on pretrained masked diffusion language models whose conditional prediction supports both crystal construction and reference-conditioned reconstruction. A lattice-conditioned periodic head couples coordinate candidates in a tractable joint distribution, making periodic compatibility an intrinsic part of draft construction. After diffusion refinement, structured records linking reference structures, executed modifications, and their physical outcomes train a reconstruction diffusion language model to propose targeted replacements and a relative verifier to assess candidates against their references. This feedback stage turns physical evaluations into reusable supervision for subsequent structural decisions. Experiments on MP-20, Perov-5, and MPTS-52 demonstrate higher draft structural validity than existing language-model constructors. On MP-20, the complete framework achieves a stable, unique, and novel (S.U.N.) rate of 10.50%, with component comparisons showing that periodic construction improves structural validity under a common diffusion refiner while feedback learning further increases discovery yield.