STRiDE: STate-space Riemannian Diffusion for Equivariant Planning

Fast and reliable motion planning is essential for robots with many degrees of freedom in complex, dynamic environments. Diffusion models offer a promising alternative to classical planners by learning informative trajectory priors. In current imitation-learning paradigms, these models are kept lightweight—lacking encoders—and trained to overfit to a single environment. As a result, adaptation relies solely on diffusion guidance, which fails under large execution-time changes or varying initializations. In addition, current approaches ignore the underlying topology of the state space thus requiring heavy guidance that dominates planning time and reduces efficiency dramatically. We introduce STRiDE, a novel diffusion motion planner that operates directly on the state space manifold and learns equivariant trajectory priors. Our approach eliminates the need for retraining under rotations around the gravity axis and enables faster convergence using Riemannian (rather than ambient) guidance. STRiDE delivers efficient, robust, and generalizable planning, overcoming key limitations of existing approaches.