Enforcing Constraints in Molecular and Crystalline Generative Models via Physics-Constrained Flow Matching

Pretrained flow-based generative models for molecules and crystals often violate hard geometric constraints at inference time, despite being trained on valid data. Herein, we extend Physics-Constrained Flow Matching (PCFM) to atomistic generative models and demonstrate it in two representative settings: (i) enforcing bond length, aromatic planarity, E/Z double bond stereochemistry, and R/S tetrahedral chirality constraints for conformer sampling, and (ii) enforcing lattice system constraints in crystal structure prediction. On GEOM-DRUGS, PCFM enforces bond length bounds and aromatic planarity while preserving ET-Flow recall and precision, and improves stereochemical pass rates by up to $14.5$%. On MP-20, conditional lattice correction with PCFM reduces unit cell mismatches and increases FlowMM's crystal structure match rate to $74.3$%. Overall, PCFM turns pretrained flow matching models into constrained samplers for molecular and crystalline generation, without finetuning or architectural changes, with broader applications to molecular and materials design currently underway.