Title: A Practical Guide for Incorporating Symmetry in Diffusion Policy
Venue: NeurIPS 2025
Accepted: yes
Keywords: Robotic Manipulation

Equivariance

Diffusion Model
Abstract: Recently, equivariant neural networks for policy learning have shown promising improvements in sample efficiency and generalization, however, their wide adoption faces substantial barriers due to implementation complexity. Equivariant architectures typically require specialized mathematical formulations and custom network design, posing significant challenges when integrating with modern policy frameworks like diffusion-based models. In this paper, we explore a number of straightforward and practical approaches to incorporate symmetry benefits into diffusion policies without the overhead of full equivariant designs. Specifically, we investigate (i) invariant representations via relative trajectory actions and eye-in-hand perception, (ii) integrating equivariant vision encoders, and (iii) symmetric feature extraction with pretrained encoders using Frame Averaging. We first prove that combining eye-in-hand perception with relative or delta action parameterization yields inherent SE(3)-invariance, thus improving policy generalization. We then perform a systematic experimental study on those design choices for integrating symmetry in diffusion policies, and conclude that an invariant representation with equivariant feature extraction significantly improves the policy performance. Our method achieves performance on par with or exceeding fully equivariant architectures while greatly simplifying implementation.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper systematically studies different approaches to incorporate symmetries (invariance/equivariance) into diffusion policies.\nSpecifically, the authors compared three action representations (abs, rel, delta), and four image encoders (cnn, equi cnn, pretrained cnn, frame averaging) using 12 robotic manipulation tasks and found that, in general, incorporating symmetries improves the performance of diffusion policies.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\nThe paper is clearly written and easy to follow.\nThe systematic evaluation of various techniques for incorporating symmetries provides practical value and can help guide practitioners in the design of network architectures and data collection pipelines.\nThe empirical results showing that equivariant diffusion policies using a single view can perform competitively with more complex voxel-based baselines are particularly interesting and suggest promising directions for future work.\n\nWeaknesses:\n\n1. The action representations proposed in this paper appear to be specifically designed for eye-in-hand robotic setups, and it remains unclear how well these techniques would generalize to other types of tasks or embodiments.\n2. One common problem with incorporating symmetries is that the tasks usually do not fully respect the group structures in general, due to factors like imperfections of the observations. I think it would be beneficial to consider soft variants like [1].\n\n[1] Finzi, Marc, Gregory Benton, and Andrew G. Wilson. \"Residual pathway priors for soft equivariance constraints.\" Advances in Neural Information Processing Systems 34 (2021): 30037-30049.\n\nQUESTIONS:\n1. How important is FOV in terms of performance? It appears that there are no direct comparison between normal FOV and large FOV in the experiments, but only large FOV and normal FOV + external/voxel.\n2. Related to (1), would it be possible to also incorporate equivariant CNNs in the normal FOV + external setting? Would it require significant changes to the architecture?\n3. How sensitive is the method's performance to the discretization of SO(2) used in equivariant CNNs? (e.g., would $C_4$ improve/degrade performance)\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-16"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes practical strategies to incorporate spatial symmetry into diffusion-based policy learning frameworks without the overhead of fully equivariant architectures. The authors demonstrate that using SE(3)-invariant representations—specifically relative trajectory actions and eye-in-hand perception—naturally leads to improved generalization. Additionally, the work introduces the use of equivariant vision encoders and Frame Averaging to leverage symmetry-aware features from pretrained networks. Across 12 tasks in the MimicGen benchmark, the proposed methods achieve performance competitive with or better than state-of-the-art equivariant policies while maintaining simplicity in design and implementation.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- The paper presents a thorough theoretical analysis backed by extensive empirical validation on a standard benchmark. Results are clearly reported and systematically compared.\n- The writing is clear and well-organized.\n- The work addresses a critical trade-off in robot learning: the complexity of incorporating symmetry versus the practical need for deployable, performant policies. This makes the contribution broadly relevant to practitioners and researchers.\n\nWeaknesses:\n- Proposition 2 assumes the policy does not depend on the gripper pose $T_t$, yet the authors themselves acknowledge this is not strictly true in practice. However, no ablation is provided to quantify how much performance degrades due to residual $T_t$-dependence. As a result, the claim that “approximate invariance” suffices remains qualitative and lacks experimental support.\n- The experimental sections evaluate combinations of techniques (e.g., relative trajectories with equivariant encoders), but do not fully isolate the contributions of each component via comprehensive ablations.\n\nQUESTIONS:\n- How much additional computational cost is introduced by Frame Averaging, and how does this compare to training from scratch with a full equivariant architecture?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes and evaluates several methods to gain the benefits of symmetry-awareness in robotic manipulation policies without the high implementation complexity of fully equivariant models.\nThe authors show that through a combination of invariant representations (eye-in-hand camera with relative actions), equivariant vision encoders and symmetrizing pretrained encoders with Frame Averaging, they can achieve performance comparable to state of the art equivariant architectures while using a much simpler and more practical setup.\n\nSTRENGTHS AND WEAKNESSES:\nSTRENGTHS:\n- The authors formally prove that the combination of eye-in-hand perception and relative actions parametrisation leads to inherent SE(3)-invariance. While components are not new, this specific formalisation is novel as far as I am aware\n- The paper does a good job at systematically analysing these known techniques and how they can be practically integrated into a feasible and effective setup for robotic learning\n- The authors obtain good results given the simpler setup, effectively, they show that for a minor drop in performance, they can disregard three RGBD cameras and the complex voxelisation / equivariance network pipeline. \n- As the title suggests, the paper provides a clear, practical guide backed by systematic experimental / empirical findings. \n\nWEAKNESSES:\n- The novelty is limited, as the authors are simply combining and analysing different known methods\n- The comparisons in Table 2 are not completely fair, as they are comparing their method (which uses an eye-in-hand camera) to EquiDiff (using absolute actions and multiple external cameras). Yes, it is a simpler setup, and the authors argue the setup is a key part of their solution, but I still find the comparison a bit awkward.\n\nQUESTIONS:\n- I think it would be interesting to see an experiment where the proposed Pretrain+FA was applied to the same multi-camera, absolute action setting as EquiDiff. Additionally, would it be possible to run EquiDiff in your eye-in-hand setup? I think having these two experiments would strengthen the paper\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-02"}

comments: SUMMARY:
This paper presents a guide on how to easily incorporate symmetry into diffusion policies. They propose a combination of in-hand camera observation, relative action commands, and equivariant image encoders. The authors evaluate their approach in simulation benchmarks and show that their simple approach offers comparable performance to fully equivariant network designs.

STRENGTHS AND WEAKNESSES:
Strength:

1. Proposes a simple yet effective way of designing diffusion policies that incorporate symmetry.
2. Clearly documents expeirments designs and results. Overall paper is clear and well presented.
3. Offers a interesting proof on how in-hand observations + relative actions leads to SE3 equivariance under assumptions.

Weakness:

1. No real-world experiment to evaluate the proposed approach.
2. Limited experimental results. The result from using relative actions is not very interesting as it was already proposed in the oringal DP paper and widely used in diffusion policies these days.
3. Action selection is well explored in the community, and the use of equivariant encoders and in-hand observations are not uncommon in robot policy learning.

QUESTIONS:
1. Since the design incorporates symmetry, will it perform better in low-data regimes? All of the datasets used are fairly abundant in the experiments.
2. As mentioned in the paper that frame averaging slows down the training process. Does it also slow down the inference process? Will it limit the performance of the policy in realworld settings if the latency of the model increases?
3. It would be interesting to see how this work can be extended to external observation cameras.

LIMITATIONS:
Yes.
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-07-03