Why robot movement policies have been geometrically wrong all along

Robot learning policies represent 3D poses (position + rotation) as simple 12-dimensional vectors, which violates the mathematical structure of rotation groups and causes the robot to drift off valid orientations. Researchers built Lie Diffuser Actor, a diffusion model that respects SE(3) geometry by operating directly on the manifold of rigid transformations. On CALVIN, a standard manipulation benchmark, it improves average task completion length from 3.27 to 3.51 steps, with gains confirmed on real hardware.