Fast, reliable and versatile motion planning algorithms are essential for robotswith many degrees of freedom in complex, dynamic environments. Diffusionmodels have been proposed as a faster alternative to classical planners by providing informative priors on distributions of trajectories. However, they are currentlytrained to overfit to environments with fixed object configurations and need to bere-trained when these conditions change. This limits applicability in tasks likerobotic manipulation where environments change dynamically and initial configurations vary. We show that diffusion-guidance is not sufficient to adapt the modelto large changes that can happen during execution or even from different initialization. Moreover, current approaches ignore the underlying topology of the statespace thus requiring heavy guidance that dominates planning time and reducesefficiency dramatically. To address these, we propose a novel diffusion motionplanner, EqM-MPD that operates directly on the robot’s state space manifold andproduces an equivariant prior distribution on trajectories. Our approach eliminates the need for retraining under rigid transformations. Moreover, our diffusion on state space manifold converges faster during guidance. We show that ourapproach achieves efficient, robust and generalizable planning that is especiallyuseful for manipulation advancing beyond prior limitations.