Few-Step Crystal Generation via Composition-Conditioned Moment Matching

Deep generative models offer a scalable route to explore the vast composition–structure search space underlying materials discovery. Existing diffusion- and flow-based crystal generators, however, still rely on long iterative sampling trajectories, limiting their use in high-throughput settings where large candidate libraries must be generated efficiently. We propose CoMMat (Composition-conditioned Moment matching for Material generation), a few-step crystal generation framework that separates chemical composition modeling from geometric refinement. Given a composition, CoMMat obtains a composition-conditioned structural latent, predicts the lattice once, and refines only atomic coordinates while keeping species and lattice fixed, reducing iterative generation to a continuous geometric transport problem. To solve this problem in only a few network evaluations, we adapt inductive moment matching to periodic crystal geometry through a lattice-normalized Cartesian transport space coupled with periodic coordinate evaluation in wrapped fractional coordinates. Conditioning the structural prior on composition eliminates the need to encode target geometry, enabling a unified few-step generator for both crystal structure prediction and de novo generation. Across the MP-20, Perov-5, Carbon-24, and MPTS-52 benchmarks, CoMMat retains strong generation quality with only 2–8 neural function evaluations. Under matched few-step budgets, it achieves favorable CSP and de novo generation performance relative to recent diffusion- and flow-based baselines, with particularly strong results at the lowest sampling budgets. At its 32-NFE setting, CoMMat remains competitive with much higher-budget baselines while substantially reducing inference cost. These results demonstrate a practical route toward scalable few-step crystal generation.