CrystalJTF: Jacobian-Pulled Gradient Guidance with Atom-Adaptive Gradient Scaling for Crystal Diffusion Models

Diffusion models offer a promising route to crystal discovery, but generating thermodynamically stable and novel structures remains challenging. Integrat- ing physical signals from pretrained interatomic potentials into sampling tra- jectories could improve generation quality without additional training. Effec- tive feedback, however, must address two challenges: the coordinate-space mis- match between predicted-endpoint forces and current sampling coordinates, and differences in local response scales across atoms in periodic systems. We pro- pose CrystalJTF, a plug-and-play, training-free guidance framework for crystal diffusion models. Point Q-JTF pulls endpoint forces back to the current sam- pling coordinates through the predicted clean endpoint map’s Jacobian trans- pose. Relative-BB uses sampling history to adapt atom-wise relative update scales, while a shared periodic geometry cap limits displacement magnitudes. CrystalJTF freezes both the generator and potential and retains native lattice and element-type sampling rules, supporting composition-conditioned and un- conditional generation. Across six benchmark settings involving CrysLLM- Gen, DiffCSP, and MatterGen, CrystalJTF consistently improves the fractions of stable or metastable, unique, and novel structures (SUN/MSUN). Under CHGNet 0.3.0 evaluation, SUN and MSUN increase by an average of 1.28 and 4.78 percentage points on MP-20, respectively, while MatterGen’s MSUN in- creases by 13.8 percentage points on Alex-MP-20. Sensitivity analyses across evaluation-potential versions and matching tolerances further support the robust- ness of these results.