LatentSpring: Harmonic Sources and Physical Corrections for Molecular Generation

Generating three-dimensional molecules from atomic composition requires learning both connectivity and geometry. We present LatentSpring, a flow-matching model that combines a harmonic-mixture source with learned geometric and physical corrections. The source samples atom positions along random auxiliary trees using element-dependent length scales, without requiring a chemical bond graph. Recovery training teaches the flow to restore perturbed geometries, while two small equivariant networks refine its predicted endpoints using reference structures and force feedback. On 64 unseen compositions, LatentSpring achieves a graph- and-force yield of 35.35% across five fits, compared with 8.75% for GAGA (Qu et al., 2026) and 8.15% for EDM (Hoogeboom et al., 2022), at a GFN2-xTB force- RMS threshold of 5 eV/ ˚ A. Adding local geometry checks gives a yield of 9.63%, compared with 4.43% for the initial force-corrected flow. This improvement holds in all three additional training repetitions, and the complete method outperforms a continuation control with matched backbone updates. The endpoint formulation also allows the trained correction networks to improve EDM and GAGA without retraining. Sampling requires only neural-network evaluations, with no energy queries or geometry optimization.