Equivariant Diffusion Policy

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.