This paper introduces Equivariant Diffusion Policy, a novel diffusion policy learning method that leverages domain symmetries to improve sample efficiency and generalization in the denoising function. The method is based on the SO(2) symmetry of full 6-DoF control and characterizes when a diffusion model is SO(2)-equivariant. The method is evaluated on 12 simulation tasks in MimicGen, achieving a success rate that is, on average, 21.9% higher than the baseline Diffusion Policy. The method is also evaluated on a real-world system, showing that effective policies can be learned with relatively few training samples. The paper also provides a theoretical analysis of the conditions under which the denoising function is equivariant and demonstrates the use of SO(2)-equivariance in the context of 6-DoF control for robotic manipulation. The method is implemented using an equivariant diffusion model with a network architecture that includes an equivariant observation encoder, an equivariant action encoder, and a denoising network. The method is evaluated in both simulation and real-world settings, showing that it outperforms the baseline Diffusion Policy in both cases. The paper also discusses the limitations of the method, including the partial utilization of the power of equivariance due to symmetry mismatch in the vision system and the potential harm of "incorrect equivariance" when the model's symmetry conflicts with the demonstration. The paper concludes that the method provides a general framework for using SO(2)-equivariance in 6-DoF control for robotic manipulation and demonstrates its effectiveness in both simulation and real-world settings.This paper introduces Equivariant Diffusion Policy, a novel diffusion policy learning method that leverages domain symmetries to improve sample efficiency and generalization in the denoising function. The method is based on the SO(2) symmetry of full 6-DoF control and characterizes when a diffusion model is SO(2)-equivariant. The method is evaluated on 12 simulation tasks in MimicGen, achieving a success rate that is, on average, 21.9% higher than the baseline Diffusion Policy. The method is also evaluated on a real-world system, showing that effective policies can be learned with relatively few training samples. The paper also provides a theoretical analysis of the conditions under which the denoising function is equivariant and demonstrates the use of SO(2)-equivariance in the context of 6-DoF control for robotic manipulation. The method is implemented using an equivariant diffusion model with a network architecture that includes an equivariant observation encoder, an equivariant action encoder, and a denoising network. The method is evaluated in both simulation and real-world settings, showing that it outperforms the baseline Diffusion Policy in both cases. The paper also discusses the limitations of the method, including the partial utilization of the power of equivariance due to symmetry mismatch in the vision system and the potential harm of "incorrect equivariance" when the model's symmetry conflicts with the demonstration. The paper concludes that the method provides a general framework for using SO(2)-equivariance in 6-DoF control for robotic manipulation and demonstrates its effectiveness in both simulation and real-world settings.