G2FM: A Geodesic Flow Matching Framework with Geometric Prior for Category-Level 9-DoF Pose Estimation

Estimating category-level 9-DoF object poses (rotation, trans-lation, scale) is fundamental for robotic manipulation and autonomoussystems. Generative approaches, particularly diffusion-based models, haveachieved strong accuracy by effectively bridging the sim-to-real domaingap through large-scale synthetic training. However, it is difficult fordiffusion-based approaches to achieve both high accuracy and real-timeperformance due to their reliance on a multi-step iterative inference pro-cess. To address this limitation, we propose Geometric Prior GeodesicFlow Matching (G2FM), an efficient, simulation-free training objectivethat learns a deterministic vector field to directly map noise to pose dis-tributions. G2FM learns a vector field mapping noise to pose distribu-tions with only three ODE steps, achieving high accuracy and real-timeperformance (> 30 FPS). To avoid the structural distortion and singular-ities caused by Euclidean approximations, we construct a geometrically-consistent trajectory that operates directly on the SO(3) manifold bytransporting rotations along geodesic paths. Furthermore, to dynami-cally refine the generative flow during inference and enhance accuracywithout retraining, we design a training-free geometric guidance mech-anism by leveraging Chamfer distance gradients to project pose correc-tions directly onto the SO(3) tangent space. Extensive experiments showthat G2FM delivers a favorable accuracy-efficiency-generalization trade-off for category-level RGB-D 9-DoF pose estimation. Code will be re-leased upon publication.