Recent advances in hierarchical policy learning highlight the advantages of decomposing systems into high-level and low-level agents, enabling efficient long-horizon reasoning and precise fine-grained control. However, the interface between these hierarchy levels remains underexplored, and existing hierarchical methods often ignore domain symmetry, resulting in the need for extensive demonstrations to achieve robust performance. To address these issues, we propose Hierarchical Equivariant Policy (HEP), a novel hierarchical policy framework. We propose a frame transfer interface for hierarchical policy learning, which uses the high-level agent's output as a coordinate frame for the low-level agent, providing a strong inductive bias while retaining flexibility. Additionally, we integrate domain symmetries into both levels and theoretically demonstrate the system's overall equivariance. HEP achieves state-of-the-art performance in complex robotic manipulation tasks, demonstrating significant improvements in both simulation and real-world settings.

Recent work has shown diffusion models are an effective approach to learning the multimodal distributions arising from demonstration data in behavior cloning. However, a drawback of this approach is the need to learn a denoising function, which is significantly more complex than learning an explicit policy. In this work, we propose Equivariant Diffusion Policy, a novel diffusion policy learning method that leverages domain symmetries to obtain better sample efficiency and generalization in the denoising function. We theoretically analyze the $\mathrm{SO}(2)$ symmetry of full 6-DoF control and characterize when a diffusion model is $\mathrm{SO}(2)$-equivariant. We furthermore evaluate the method empirically on a set of 12 simulation tasks in MimicGen, and show that it obtains a success rate that is, on average, 21.9% higher than the baseline Diffusion Policy. We also evaluate the method on a real-world system to show that effective policies can be learned with relatively few training samples, whereas the baseline Diffusion Policy cannot.