Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition
2026-05-25 • Machine Learning
Machine LearningArtificial Intelligence
AI summaryⓘ
The authors explain that current methods for creating 3D shapes of molecules treat them like loose groups of points, missing how molecules really move—mostly by twisting rather than stretching or bending a lot. They introduce GO-Flow, which breaks down molecule generation into parts that match real movements: sliding, rotating, and twisting. This approach respects the natural geometry of molecules and helps produce more realistic shapes faster. Tests show their method makes better and more accurate molecules using fewer steps.
3D molecular conformationdiffusion modelsmanifold decompositionoptimal transportSO(3) rotation groupequivariant neural networksbond anglestorsion anglesgeometric inductive biascomputational chemistry
Authors
Yunqing Liu, Yi Zhou, Wenqi Fan
Abstract
The generation of accurate 3D molecular conformations is a pivotal challenge in computational chemistry and drug discovery. Recently, diffusion and flow matching models have achieved remarkable success. However, there is a critical misalignment between their mathematical formulation and the physical reality of molecules. Existing approaches predominantly treat molecules as unstructured point clouds in Cartesian space, overlooking the intrinsic hierarchical mechanics where bond lengths and bond angles are relatively stiff, whereas torsion angles constitute the dominant flexible degrees of freedom. This lack of manifold awareness forces models to relearn fundamental geometric constraints from scratch, often leading to physically implausible intermediate structures. To address this, we propose GO-Flow that aligns generative modeling with molecular geometry via manifold decomposition. Instead of forcing motion through Euclidean space, GO-Flow decomposes the generation process into three physically motivated subspaces: translation space with linear optimal transport, rotation space with geodesic flows on $SO(3)$, and conformation space with entropic optimal transport. This decomposition injects geometric inductive biases and makes the generative paths better aligned with molecular degrees of freedom. When combined with equivariant neural architectures, it encourages rotation-consistent generation and improves geometric validity. Extensive experiments on GEOM-Drugs and GEOM-QM9 demonstrate that GO-Flow achieves state-of-the-art generation quality. Notably, by learning straighter probability paths on the correct manifolds naturally, our method enables high-fidelity sampling with as few as 50 steps, effectively bridging the gap between structural precision and computational efficiency.