# Equivariant Volumetric Grasping

arXiv: https://arxiv.org/abs/2507.18847 · HTML: https://mlsanity.com/paper/2507.18847/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 47 references that are in the map.
- First posted on arXiv 24 Jul 2025.

## Builds on (most cited first, 30 of 37)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Deformable ConvNets v2: More Deformable, Better Results](https://mlsanity.com/paper/1811.11168/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [6-DOF GraspNet: Variational Grasp Generation for Object Manipulation](https://mlsanity.com/paper/1905.10520/) (2019)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [Grasp Pose Detection in Point Clouds](https://mlsanity.com/paper/1706.09911/) (2017)
- [Synergies Between Affordance and Geometry: 6-DoF Grasp Detection via Implicit Representations](https://mlsanity.com/paper/2104.01542/) (2021)
- [Volumetric Grasping Network: Real-time 6 DOF Grasp Detection in Clutter](https://mlsanity.com/paper/2101.01132/) (2021)
- [Roto-Translation Covariant Convolutional Networks for Medical Image Analysis](https://mlsanity.com/paper/1804.03393/) (2018)
- [PointNetGPD: Detecting Grasp Configurations from Point Sets](https://mlsanity.com/paper/1809.06267/) (2018)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (2021)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [S4G: Amodal Single-view Single-Shot SE(3) Grasp Detection in Cluttered Scenes](https://mlsanity.com/paper/1910.14218/) (2019)
- [Graspness Discovery in Clutters for Fast and Accurate Grasp Detection](https://mlsanity.com/paper/2406.11142/) (2024)
- [DexGraspNet 2.0: Learning Generative Dexterous Grasping in Large-scale Synthetic Cluttered Scenes](https://mlsanity.com/paper/2410.23004/) (2024)
- [Edge Grasp Network: A Graph-Based SE(3)-invariant Approach to Grasp Detection](https://mlsanity.com/paper/2211.00191/) (2022)
- [Imagination Policy: Using Generative Point Cloud Models for Learning Manipulation Policies](https://mlsanity.com/paper/2406.11740/) (2024)

## Built on by (most cited first, 1 of 1)

- [Spatial Memory for Out-of-Vision Manipulation in Vision-Language-Action](https://mlsanity.com/paper/2605.22283/) (2026)

## Abstract (arXiv)

We propose a new volumetric grasp model that is equivariant to rotations around the vertical axis, leading to a significant improvement in sampling efficiency. Our model employs a tri-plane volumetric feature representation -- i.e., the projection of 3D features onto three canonical planes. We introduce a novel tri-plane feature design in which features on the horizontal plane are equivariant to 90^circ rotations, while the sum of features from the other two planes remains invariant to reflections induced by the same transformations. We further develop equivariant adaptations of two state-of-the-art volumetric grasp planners, GIGA and IGD. Specifically, we derive a new equivariant formulation of IGD's deformable attention mechanism and propose an equivariant generative model of grasp orientations based on flow matching. We provide a detailed analytical justification of the proposed equivariance properties and validate our approach through extensive simulated and real-world experiments. Our results demonstrate that the proposed projection-based design reduces both computational and memory costs. Moreover, the equivariant grasp models built on top of our tri-plane features consistently outperform their non-equivariant counterparts, achieving higher performance within a real-time cost constraint. Video and code can be viewed in: https://mousecpn.github.io/evg-page/