Fig. 2: Performance comparison between structures generated by CrystalFlow and the previous Cond-CDVAE²⁶ model.

CrystalFlow is trained on the MP-CALYPSO-60 dataset (see Results section C). Integration steps of S = 100, 1000, and 5000 are utilized for CrystalFlow, while S = 5000 is employed for Cond-CDVAE. a Hexagonal binned histograms of the relationship between the density functional theory (DFT) computed lattice stress and the target pressure for 500 structures generated by each model. The composition and target pressure are randomly sampled from the test set. b Distributions of enthalpy (H) differences for these structures before and after local optimization. c Average energy curves during local optimization for 200 SiO₂ structures generated by each model at 0 GPa, with shaded areas denoting standard deviation. d Energy distributions of these SiO₂ structures before and after local optimization. Source data are provided as a Source Data file.