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EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning

Jingyun Yang, Zi-ang Cao, Congyue Deng, Rika Antonova, Shuran Song, Jeannette Bohg

arXiv:2407.01479v2cs.ROcs.LG

TL;DR

Imitation-learned visuomotor policies require substantial data and generalize poorly to unseen scenarios. EquiBot combines SIM(3)-equivariant networks with diffusion policies for manipulation. Across simulated and real-world tasks, it generalizes to unseen scenarios after five minutes of demonstrations per task, while remaining limited on several kinds of scene variation.

  • Problem

    Imitation-learned visuomotor policies work in controlled settings but require substantial data and generalize poorly to unseen scenarios, limiting practical deployment.

    Source: §1 · p. 1

  • Method

    EquiBot combines SIM(3)-equivariant neural networks with diffusion policies to predict actions that transform with inputs while supporting multi-modal behavior.

    Source: §1 · pp. 1–2

  • Results

    Across six simulated and six real robot tasks, EquiBot outperforms vanilla diffusion policies and prior equivariant imitation methods and generalizes to unseen scenarios from five minutes of demonstrations.

    Source: §1 · p. 2, §5 · p. 8

  • Takeaways & Limitations

    EquiBot generalizes to unseen objects and scenes in the reported mobile-manipulation tasks after five minutes of human demonstrations per task.

    Source: §1 · p. 2

    EquiBot does not handle nonlinear changes in object shape or dynamics, changes in relative object positioning, partial occlusion, or dramatic camera-angle changes.

    Source: §5 · p. 8

Abstract

from arXiv · show

Building effective imitation learning methods that enable robots to learn from limited data and still generalize across diverse real-world environments is a long-standing problem in robot learning. We propose Equibot, a robust, data-efficient, and generalizable approach for robot manipulation task learning. Our approach combines SIM(3)-equivariant neural network architectures with diffusion models. This ensures that our learned policies are invariant to changes in scale, rotation, and translation, enhancing their applicability to unseen environments while retaining the benefits of diffusion-based policy learning such as multi-modality and robustness. We show on a suite of 6 simulation tasks that our proposed method reduces the data requirements and improves generalization to novel scenarios. In the real world, with 10 variations of 6 mobile manipulation tasks, we show that our method can easily generalize to novel objects and scenes after learning from just 5 minutes of human demonstrations in each task.

1 Introduction

EquiBot addresses the data demands and poor unseen-scenario generalization of imitation-learned visuomotor policies. It combines equivariant neural networks with diffusion policies and is evaluated in simulation and real-world mobile manipulation.

1 Introduction

  • Imitation-learned visuomotor policies work in controlled settings but require substantial data and generalize poorly to unseen scenarios, limiting practical deployment.The introduction frames real-world environmental unpredictability and variability as central challenges.Source: §1 · p. 1
  • EquiBot combines diffusion policies with equivariant networks whose outputs scale, translate, and rotate with inputs, supporting generalization to unseen object visuals, sizes, and placements.The architecture is described as equivariant even if not fully trained.Source: §1 · pp. 1–2
  • Diffusion-based policy learning supports robust performance, idle actions, and multi-modal behaviors, while EquiBot can infer actions for in-distribution placements and poses that were insufficiently demonstrated.At test time, it uses single-view, object-centric point clouds and robot proprioception to predict sequences of end-effector velocity commands and gripper signals.Source: §1 · p. 2
  • In six simulated tasks and six real-world mobile manipulation tasks, EquiBot generalizes to unseen scenarios and objects from just five minutes of human demonstrations.The real-world evaluation includes unseen objects and scenes and outperforms baselines relying on augmentation or non-diffusion action prediction.Source: §1 · p. 2

2 Related Work

Prior work addresses data efficiency and generalization through few-shot learning, augmentation, equivariant policies, and equivariant diffusion models. EquiBot combines SIM(3)-equivariance with diffusion for closed-loop 3D manipulation from point clouds.

Data-efficient imitation learning

  • Few-shot imitation methods use multi-task demonstrations, while sampling-based methods can be limited to small action spaces and open-loop settings; EquiBot instead embeds equivariance in the policy architecture.The authors state that this can improve data efficiency and support robust policies learned from a handful of demonstrations.Source: §2 · p. 2

Equivariance in robot manipulation

  • Prior equivariant manipulation methods often lack closed-loop policies or scale equivariance, while EquiAct is deterministic and cannot handle multi-modal training data or predict multiple future actions.EquiBot is presented as training stably, handling multi-modal data with diffusion, and generalizing across appearance, initial states, scales, and poses.Source: §2 · p. 2

Equivariant diffusion architectures

  • EquiBot proposes an equivariant diffusion policy for closed-loop 3D manipulation tasks using point-cloud observations.The related-work comparison presents this as a contrast to prior equivariant diffusion approaches with more limited task or observation settings.Source: §2 · pp. 2–3

3 Method

EquiBot makes a diffusion policy equivariant by construction, so transformed observations yield correspondingly transformed actions. It combines an equivariant diffusion process with point-cloud and robot-state representations normalized for SIM(3) transformations.

3.2 Equivariant Distributions and Diffusion

  • EquiBot makes each diffusion step equivariant, yielding an equivariant action distribution under stochasticity.The method uses an equivariant noise-prediction network; its Gaussian action prior is also SO(3)-equivariant.Source: §3 · p. 3, §3.2 · p. 4

3.1 Preliminaries

  • The policy conditions on scene point clouds and robot proprioception, and learns to predict the next action or a future action sequence.Actions and proprioception are represented using 3D positions or offsets, normalized directions, and scalars.Source: §3.1 · pp. 3–4
  • The method represents actions with a denoising process that starts from Gaussian noise and iteratively predicts less noisy actions conditioned on observations.The CNN-based policy uses an observation encoder, diffusion-step positional embeddings, FiLM conditioning, and a convolutional U-net to predict denoising gradients.Source: §3.1 · pp. 3–4

3.2 Equivariant Distributions and Diffusion

  • The per-step equivariance argument focuses on SO(3); canonicalization before diffusion extends the architecture to translation and scale.Equivariant Markov transitions and an equivariant prior yield an equivariant final action distribution.Source: §3.2 · p. 4

3.3 SIM(3)-Equivariant Diffusion Policy

  • EquiBot adapts a CNN-based diffusion policy by making its encoder SIM(3)-equivariant and its FiLM layers, U-net, and connecting layers SO(3)-equivariant.The encoder supplies an object centroid and scale for normalizing inputs and restoring the output actions.Source: §3.1 · p. 3, §3.3 · pp. 4–5

4 Experiments

The experiments test generalization, robustness, data efficiency, and component contributions in simulation and on real robots. Across the reported settings, EquiBot is compared with diffusion and equivariant-policy baselines under varied tasks and evaluation conditions.

4 Experiments

  • The experiments are designed to assess generalization, robustness, data efficiency, and component contributions using quantitative simulation and real-world evaluations.The experiments section points to supplementary ablations for component analysis.Source: §4 · p. 5

4.1.1 Comparisons to Vanilla Diffusion Policies and Other Equivariant Policy Architectures

  • The simulation comparison includes DP, DP+Aug, and EquivAct across four tasks, with rotation, scale, and translation changes in the OOD evaluation setups.The tasks include mobile manipulation of deformable and articulated objects and the multimodal Push T benchmark.Source: §4.1.1 · pp. 5–6
  • EquiBot is stable across four simulation tasks and has the least performance drop across OOD setups, while DP+Aug and EquivAct show task-specific weaknesses.DP+Aug drops on position and combined OOD shifts; EquivAct struggles with Push T's multimodal data.Source: §4.1.1 · pp. 6–7, Figure 4 · p. 6

4.1.2 Data Efficiency Experiments

  • As demonstrations decrease from 100 to 25 in both tasks, Diffusion Policy performance drops dramatically, while the proposed method retains relatively higher performance, indicating better data efficiency.The authors attribute this to the method’s equivariance helping it cope with novel initial object poses at test time when training data do not cover their full distribution.Source: §4.1.2 · p. 7

4.2 Real Robot Experiments

  • The real-world suite covers six mobile manipulation tasks, with evaluation conditions varying from in-distribution scenes to novel objects and translated or rotated layouts.Each method is evaluated for 10 episodes per task.Source: §4.2 · pp. 7–8, Figure 6 · p. 8
  • Across six real-robot tasks, EquiBot learns from 5 minutes of human demonstrations and outperforms Diffusion Policy and Diffusion Policy with Augmentation by a large margin.Evaluations include unseen objects and poses in both in-distribution and out-of-distribution scenarios.Source: Table 1 · p. 8, §4.2 · p. 8

5 Conclusions, Limitations and Future work

EquiBot is presented as a data-efficient, generalizable visuomotor policy for robot manipulation. Its supported generalization scope has concrete boundaries in object shape, dynamics, and multi-object arrangements.

5 Conclusions, Limitations and Future work

  • Across six simulated and six real-robot tasks, EquiBot outperforms vanilla diffusion policies and prior imitation-learning methods using equivariant architectures.The paper reports learning from five minutes of human demonstrations and generalizing to scenarios dramatically different from training.Source: §5 · p. 8
  • EquiBot generalizes to unseen object positions, scales, and orientations, but does not handle nonlinear changes in object shape or dynamics by construction.The authors also identify variation in relative object positioning, partial occlusion, and dramatic camera-angle changes as limitations.Source: §5 · p. 8
  • The authors identify modeling scene dynamics and individual objects, and learning robust 3D representations, as possible directions for addressing these limitations.They also name extending to multi-task setups as future work.Source: §5 · p. 8

A Further Discussion of Related Works

The discussion compares EquiBot with 3D Diffusion Policy and other equivariant manipulation approaches. It reports that equivariance can be combined with the DP3 encoder while retaining comparable Cloth Folding performance.

A Further Discussion of Related Works

  • DP3 uses a simpler encoder and a two-layer MLP for proprioception before concatenating it with the point-cloud representation.The paper describes DP3 as similar to its DP baseline, with these two architectural differences.Source: A Further Discussion of Related Works · p. 13
  • DP3 performs well in-distribution but poorly out-of-distribution, much like the paper’s DP baseline.DP3 replaces the DP baseline’s PointNet encoder with the DP3 encoder proposed in [44].Source: A Further Discussion of Related Works · p. 13, Figure 7 · p. 13
  • EquiBot with an SO(3)-equivariant DP3 encoder has slightly lower but comparable performance to EquiBot in Cloth Folding.The comparison demonstrates that the DP3 encoder can be integrated by replacing EquiBot’s PointNet-based encoder.Source: A Further Discussion of Related Works · p. 13, Figure 7 · p. 13
  • Compared with prior equivariant manipulation approaches, EquiBot supports position, orientation, and uniform scaling equivariance across rigid, deformable, and articulated-object tasks.The cited prior work includes pick-and-place and SO(2)-equivariant tabletop policies.Source: A Further Discussion of Related Works · p. 13

B Ablations and Analysis

The ablations compare EquiBot’s architecture with a diffusion-head extension of EquivAct, test individual equivariances, and examine training stability. EquiBot performs best across the reported architecture comparisons, while removing any tested equivariance hurts performance in the corresponding out-of-distribution setting.

B Ablations and Analysis

  • EquiBot performs best across the reported architecture comparisons and significantly outperforms naive EquivAct extensions in tested out-of-distribution setups.The comparison covers the hyperparameter variations tried by the authors.Source: B Ablations and Analysis · pp. 13–14, Figure 8 · p. 13
  • With prediction horizon 1, the naive diffusion-head EquivAct policy cannot generate multiple actions for temporal consistency; larger horizons cause dramatic performance drops.The authors note that EquivAct was not designed for large prediction horizons.Source: B Ablations and Analysis · p. 14
  • Removing rotation, translation, or scale equivariance causes performance drops when evaluation is out-of-distribution to the equivariance retained.The ablation was conducted on Object Covering.Source: B Ablations and Analysis · p. 14, Figure 9 · p. 14
  • EquiBot has more stable training performance across checkpoints than EquivAct on the Push T task.The comparison plots in-distribution average reward over 40 evaluation episodes every 50 training epochs.Source: B Ablations and Analysis · p. 14, Figure 10 · p. 14

C.1 Failure Analysis

The failure analysis identifies execution and perception problems across real-robot tasks, while additional results compare laundry-door performance and show rollout examples. The appendix also argues that equivariant diffusion transitions preserve equivariance in the resulting conditional distribution.

C.1 Failure Analysis

  • Packing failures commonly involve premature gripper opening; shorts failures split between late opening and friction preventing release.The authors suggest more capable deformable-object end-effectors or online adaptation as possible remedies, both outside this work’s scope.Source: §C.1 · p. 14
  • Push Chair, Laundry Door Closing, and Bimanual Folding failures often involve incomplete motions or mistimed gripper actions; Make Bed failures include incomplete comforter segmentation.The authors attribute execution failures as likely arising from accumulated action-prediction errors and resulting out-of-distribution observations; folded comforters can look like two overlapping cloth pieces to segmentation.Source: §C.1 · pp. 14–15

C.2 Additional Real Robot Results

  • The laundry-door comparison reports lower success and greater accumulated missing angle for DP than EquiBot, with more safety issues requiring manual termination for DP.The passage defines four measures: success rate, closure with click sound, total accumulated missing angle, and collision or safety issue.Source: §C.2 · p. 15, Table 2 · p. 15
  • Figure 12 presents rollout samples for the real-robot evaluation scenarios and a bonus task in which two robots lift a woven basket onto a coffee table.The listed examples include chair pushing, clothing packing, luggage closing, folding, and bed making.Source: §C.2 · p. 15, Figure 12 · p. 16

D Equivariant Distributions and Diffusion

  • The appendix proves conditional diffusion equivariance by showing that an equivariant initial distribution and equivariant Markov transitions yield an equivariant marginal distribution.The proof section presents this as the conditional counterpart to the invariant-distribution result for a Markov chain.Source: D Equivariant Distributions and… · pp. 16–17

E Method Architectures and Implementation Detail

The implementation combines an equivariant point-cloud policy with human-demonstration parsing and a mobile-robot execution pipeline. It details the network and normalization choices, hand-to-point-cloud alignment, and latency-aware action execution.

E Method Architectures and Implementation Detail

  • The policy uses 13-dimensional proprioception and 7-dimensional actions per robot, except Push T, which uses 3D position for both state and action.The standard proprioception includes end-effector position and orientation, gravity direction, and gripper opening; actions encode position velocity, angular velocity, and gripper action. The policy uses observation, prediction, and action horizons of 2, 16, and 8 steps, respectively, and real-robot inference uses DDIM with 8 denoising steps.Source: E Method Architectures and… · pp. 17–18
  • The architecture processes position, direction, and scalar information separately, scales position features to position- and scale-invariant values, then predicts denoised actions with an SO(3)-equivariant conditional U-net.The encoder is a SIM(3)-equivariant PointNet++ with four layers and hidden dimension 128 for most tasks; Push T uses two layers.Source: E Method Architectures and… · pp. 17–18, Figure 13 · p. 18
  • The authors normalize 3D-vector inputs together using mean point-cloud and action scales, then multiply the scales back before returning outputs.They state this keeps diffusion actions within the −1 to 1 range; scalar information is normalized as in vanilla diffusion policy.Source: E Method Architectures and… · pp. 18–19

F.1 Human Demo Parsing Infrastructure

  • Human demonstrations are parsed into object point clouds and hand keypoints, then aligned so the inferred finger pose shares the point-cloud coordinate frame.The authors identify alignment as crucial because hand detection and point clouds use different coordinate frames; the system uses Grounded Segment Anything with DEVA and HaMeR.Source: §F.1 · p. 19

F.2 Mobile Robot Control Infrastructure

  • A workstation parses single-camera observations, downsamples segmented point clouds to 1024 points, and sends them with proprioception for 16-action policy predictions.The robot execution process skips stale predicted actions when latency exceeds a threshold, then executes the following 8 actions.Source: §F.2 · pp. 19–20
  • On the mobile robots, control signals are transformed from the global frame to the arm’s local frame and converted into arm velocity commands.A motion-capture system supplies mobile-base position; the base moves only when the end-effector is too close to or too far from it.Source: §F.2 · p. 20

F.3 Task Details

The real-world tasks test manipulation across changes in object size, shape, or placement, with success defined separately for each task.

Push chair

  • Chair pushing uses demonstrations at a 48 × 30-inch standing desk and evaluates success at a 58×23-inch rectangular desk or 36-inch-diameter circular table.Success means the chair center goes beneath the desk.Source: §F.3 · p. 20

Luggage packing

  • Luggage packing tests four items, from the demonstrated white t-shirts to a gray towel roll, blue cap, and navy shorts.Success requires at least half of the packed object to end up inside the luggage.Source: §F.3 · p. 20

Luggage closing

  • Luggage closing transfers demonstrations on a 55 × 40 × 23 cm carry-on to a 76 × 48 × 25 cm check-in suitcase.Success means the luggage ends closed.Source: §F.3 · p. 20

Laundry door closing

  • Laundry-door closing uses the same front-loader for demonstrations and evaluation, starting with its door open.Success requires the door opening to be at most 5 cm.Source: §F.3 · p. 20

Bimanual folding

  • Bimanual folding transfers demonstrations on a 34 × 38 cm cloth to folding a 140 × 75 cm gray towel.Success requires mean grasped-corner distance to target corners below 0.2 times the cloth’s folding-side length.Source: §F.3 · p. 20

Bimanual make bed

  • Bimanual bed-making transfers demonstrations unfolding a 34 × 38 cm towel to unfolding a much larger comforter on a bed.Success requires mean grasped-corner distance to the headboard below 0.2 times the bed’s length.Source: §F.3 · p. 20

G Simulation Tasks – Further Details

The simulated-task details define task-specific reward measures for cloth folding, object covering, box closing, and Push T, while Robomimic tasks retain their original specifications.

Cloth folding

Object covering

  • Object Covering rewards the ratio of the box–cloth convex-hull intersection volume to the cloth’s convex-hull volume.Demonstrations move a 27.5 × 27.5 cm cloth onto a 10 × 7 × 5 cm rigid box.Source: G Simulation Tasks – Further Details · p. 20

Box closing

  • Box Closing scores the average closure angle of its three flaps as (a1 + a2 + a3)/(3×180).The demonstrated box measures 14.5 × 12 × 11.5 cm, and a1 to a3 are flap closure angles in degrees.Source: G Simulation Tasks – Further Details · p. 20

Push T

Robomimic tasks

H Limitations and Future Work – Further Details

Although EquiBot enforces SIM(3) equivariance by construction, the authors observed generalization to geometric variations beyond SIM(3), including non-uniform scaling.

H Limitations and Future Work – Further Details

  • EquiBot showed observed generalization to non-uniform scaling, which is not enabled by its SIM(3)-equivariance construction.The authors hypothesize that equivariance across policy layers may support more general feature representations and propose systematic probing of intermediate features as future work.Source: H Limitations and Future Work –… · p. 21

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