Geometric Flow Matching for Molecular Conformation Generation via Manifold Decomposition

2026-05-25

AI Summary

This work addresses the limitation of existing molecular conformation generation methods, which treat molecules as unstructured point clouds in Euclidean space and neglect their intrinsic geometric hierarchy, often yielding physically implausible generation trajectories. To overcome this, the authors propose a manifold-decomposition-based flow matching framework that explicitly incorporates molecular geometric priors into the generative process. The conformation generation is decoupled into three subspaces—translation, rotation, and flexible degrees of freedom—modeled respectively by linear optimal transport, SO(3) geodesic flows, and entropic optimal transport. Integrating equivariant neural networks with Lie group geometry, the method achieves state-of-the-art performance on GEOM-Drugs and GEOM-QM9, generating high-fidelity conformations in just 50 steps while significantly enhancing both physical plausibility and computational efficiency.

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.

Problem

• molecular conformation generation
• geometric flow matching
• manifold decomposition
• torsion angles
• geometric constraints

Innovation

• manifold decomposition
• geometric flow matching
• molecular conformation generation
• equivariant neural networks
• optimal transport