Flow6D: Lie-Group Consistent Riemannian Flow-Matching for Category-Level 6D Object Pose and Size Estimation

Abstract

Category-level object pose and size estimation is a critical capability for robotic manipulation in unstructured 3D environments. However, existing methods struggle to maintain stable and accurate pose predictions when handling intra-class shape variations and complex spatial transformations. To address this challenge, we propose Flow6D, a Riemannian flow matching-based framework for category-level pose and size estimation, trained solely on synthetic data. Specifically, Flow6D models pose transformations on the SE(3) Riemannian manifold, explicitly preserving the compositionality and continuity of rotations and translations, thereby improving generalization to unseen objects. To further enhance geometric equivariance, we introduce a Lie-group consistency mechanism that constructs a closed transformation set in the Sim(3) group and incorporates group structure constraints, enabling the learning of composable, invertible, and continuous geometric transformations. Additionally, Flow6D integrates a geometric prediction and encoding module and a conditional attention mechanism, which respectively refine geometric feature extraction and dynamically adapt feature interactions, improving pose estimation accuracy and robustness. Extensive quantitative and qualitative experiments on REAL275 and Wild6D, as well as real-world robotic grasping tasks with the Franka robotic arm, demonstrate the effectiveness and practical applicability of Flow6D.