UniFlowDock: Flexible Docking with Complete Equivariant Velocity Fields

Flexible molecular docking is crucial for drug discovery; however, existing flow-matching generative models often produce physically invalid conformations (e.g., steric clashes, distorted bond geometry). Our analysis suggests that a primary contributor to this challenge lies at the modeling level: when the flow is parameterized by standard equivariant networks, an intrinsic approximation floor can emerge, potentially hindering the learned velocity field from reaching its optimal convergence bound, particularly for highly flexible molecules. We present UniFlowDock, which addresses this by introducing strictly Complete Equivariant Velocity Fields, thereby eliminating the dimensional incompleteness of standard architectures. This theoretical completeness is further bolstered by Fragment-Adaptive Optimal Coupling, a method that structurally linearizes transport trajectories and decomposes the generation process into physics-aware subproblems. Experiments on PDBBind and PoseBusters demonstrate UniFlowDock achieves state-of-the-art accuracy and physical validity, showing consistent gains in highly flexible docking scenarios where target distributions exhibit higher transport complexity.