Fig. 4: MolEdit yields diverse and realistic 3D chemical structures via preference alignment and self-improvement.

a The distribution of Molecular Physics Instability (MPI) under the general AMBER force field³⁸ for 10,000 molecules generated by the E(3) equivariant diffusion model (EDM)²⁴, MolEdit with different solvers, and MolEdit with the Boltzmann-Gaussian mixture (BGM) kernel, all trained on the QM9 dataset. b The reduction in MPI when using the BGM kernel with different temperatures. Statistical distributions were derived from a sample of 10,000 molecules. Box plots in a, b are defined by the median as the center black line, first and third quartiles as the box edges and 1.5 times the interquartile range as the whiskers. c Application of the BGM kernel produces molecules with high physical stability. d MolEdit is utilized to sample diverse conformers for molecules with complex structures, which is challenging for tools like RDKit⁴⁷. e Distributions of diversity and physical stability (under universal force field)³⁷ of conformers sampled by GeoDiff³⁶, MolEdit, MolEdit with FPS solver, and RDKit on the GeoDiff test set (1024 conformations for each molecule, 1000 molecules in total). f MolEdit constructs structures with constrained cyclohexane rings in twist-boat or chair conformations and double bonds in E or Z conformations. Structures of highlighted areas are constrained during generation. Source data are provided as a Source Data file.