  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.
