Empirical Geometric Priors for Structure-Based Molecular Diffusion

Diffusion models for molecular generation are trained mainly as density estimators; where physical guidance is added, it usually takes an analytic form applied with one functional shape across atom types. We test whether empirical geometric priors, re-estimated from each training set, transfer to structure-based ligand generation. Local intramolecular, global protein--ligand, and compactness priors are added as auxiliary training losses to two backbones. Across 27 weight configurations on CrossDocked pockets, and a smaller two-condition check on PDBbind, the priors are not interchangeable: the global prior gives the best geometric fidelity, the compactness prior the largest apparent affinity gain, the local prior the broadest improvement. Compactness increases rather than prevents geometric fragmentation, and its affinity benefit reverses under a survivorship-aware hit rate. Eight of twelve two-prior combinations underperform their better component. The backbone's own Lennard--Jones term matches the priors on chemistry heuristics but reproduces neither geometric gain: the empirical construction improves distance fidelity where the analytic form does not.