SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space

Xupeng Zhu, Fan Wang, Robin Walters, Jane Shi
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:80187-80206, 2025.

Abstract

Diffusion Policies are effective at learning closed-loop manipulation policies from human demonstrations but generalize poorly to novel arrangements of objects in 3D space, hurting real-world performance. To address this issue, we propose Spherical Diffusion Policy (SDP), an SE(3) equivariant diffusion policy that adapts trajectories according to 3D transformations of the scene. Such equivariance is achieved by embedding the states, actions, and the denoising process in spherical Fourier space. Additionally, we employ novel spherical FiLM layers to condition the action denoising process equivariantly on the scene embeddings. Lastly, we propose a spherical denoising temporal U-net that achieves spatiotemporal equivariance with computational efficiency. In the end, SDP is end-to-end SE(3) equivariant, allowing robust generalization across transformed 3D scenes. SDP demonstrates a large performance improvement over strong baselines in 20 simulation tasks and 5 physical robot tasks including single-arm and bi-manual embodiments. Code is available at https://github.com/amazon-science/Spherical_Diffusion_Policy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhu25u, title = {{SE}(3)-Equivariant Diffusion Policy in Spherical {F}ourier Space}, author = {Zhu, Xupeng and Wang, Fan and Walters, Robin and Shi, Jane}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {80187--80206}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhu25u/zhu25u.pdf}, url = {https://proceedings.mlr.press/v267/zhu25u.html}, abstract = {Diffusion Policies are effective at learning closed-loop manipulation policies from human demonstrations but generalize poorly to novel arrangements of objects in 3D space, hurting real-world performance. To address this issue, we propose Spherical Diffusion Policy (SDP), an SE(3) equivariant diffusion policy that adapts trajectories according to 3D transformations of the scene. Such equivariance is achieved by embedding the states, actions, and the denoising process in spherical Fourier space. Additionally, we employ novel spherical FiLM layers to condition the action denoising process equivariantly on the scene embeddings. Lastly, we propose a spherical denoising temporal U-net that achieves spatiotemporal equivariance with computational efficiency. In the end, SDP is end-to-end SE(3) equivariant, allowing robust generalization across transformed 3D scenes. SDP demonstrates a large performance improvement over strong baselines in 20 simulation tasks and 5 physical robot tasks including single-arm and bi-manual embodiments. Code is available at https://github.com/amazon-science/Spherical_Diffusion_Policy.} }
Endnote
%0 Conference Paper %T SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space %A Xupeng Zhu %A Fan Wang %A Robin Walters %A Jane Shi %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhu25u %I PMLR %P 80187--80206 %U https://proceedings.mlr.press/v267/zhu25u.html %V 267 %X Diffusion Policies are effective at learning closed-loop manipulation policies from human demonstrations but generalize poorly to novel arrangements of objects in 3D space, hurting real-world performance. To address this issue, we propose Spherical Diffusion Policy (SDP), an SE(3) equivariant diffusion policy that adapts trajectories according to 3D transformations of the scene. Such equivariance is achieved by embedding the states, actions, and the denoising process in spherical Fourier space. Additionally, we employ novel spherical FiLM layers to condition the action denoising process equivariantly on the scene embeddings. Lastly, we propose a spherical denoising temporal U-net that achieves spatiotemporal equivariance with computational efficiency. In the end, SDP is end-to-end SE(3) equivariant, allowing robust generalization across transformed 3D scenes. SDP demonstrates a large performance improvement over strong baselines in 20 simulation tasks and 5 physical robot tasks including single-arm and bi-manual embodiments. Code is available at https://github.com/amazon-science/Spherical_Diffusion_Policy.
APA
Zhu, X., Wang, F., Walters, R. & Shi, J.. (2025). SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:80187-80206 Available from https://proceedings.mlr.press/v267/zhu25u.html.

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