Neural SHAKE: Geometric Constraints in Graph Generative Models

Generating accurate molecular conformations requires efficient sampling from the global space of atomic arrangements, which grows exponentially with the number of degrees of freedom. Incorporating prior information about geometric patterns, such as distances, angles, and dihedrals, is crucial for ensuring the accurate physical characteristics of molecules by increasing the likelihood of sampling low-energy conformations. These geometric patterns often translate into non-linear constraint satisfaction problems. We propose an innovative approach to integrate these constraints into neural differential equations using the denoising diffusion framework. By projecting the dynamics onto constrained subspaces, our method enables the generation of molecular conformations that adhere to strict geometric constraint, in contrast to similar research based on probabilistic guidance that acts as a soft prior. This technique not only enhances molecular generation methods by producing lower energy structures and more relevant conformations by sampling from subspaces but also formally generalizes classifier guidance.