# GAGrasp: Geometric Algebra Diffusion for Dexterous Grasping

arXiv: https://arxiv.org/abs/2503.04123 · HTML: https://mlsanity.com/paper/2503.04123/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 57 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [6-DOF GraspNet: Variational Grasp Generation for Object Manipulation](https://mlsanity.com/paper/1905.10520/) (2019)
- [Diffusion-based Generation, Optimization, and Planning in 3D Scenes](https://mlsanity.com/paper/2301.06015/) (2023)
- [A General Theory of Equivariant CNNs on Homogeneous Spaces](https://mlsanity.com/paper/1811.02017/) (2018)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [GPU-Accelerated Robotic Simulation for Distributed Reinforcement Learning](https://mlsanity.com/paper/1810.05762/) (2018)
- [ContactGrasp: Functional Multi-finger Grasp Synthesis from Contact](https://mlsanity.com/paper/1904.03754/) (2019)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Synthesizing Diverse and Physically Stable Grasps with Arbitrary Hand Structures using Differentiable Force Closure Estimator](https://mlsanity.com/paper/2104.09194/) (2021)
- [DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting](https://mlsanity.com/paper/2105.12244/) (2021)
- [GenDexGrasp: Generalizable Dexterous Grasping](https://mlsanity.com/paper/2210.00722/) (2022)
- [Clifford Group Equivariant Neural Networks](https://mlsanity.com/paper/2305.11141/) (2023)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [Grasp'D: Differentiable Contact-rich Grasp Synthesis for Multi-fingered Hands](https://mlsanity.com/paper/2208.12250/) (2022)

## Built on by (most cited first, 8 of 8)

- [Diffusion Models for Robotic Manipulation: A Survey](https://mlsanity.com/paper/2504.08438/) (2025)
- [Hybrid Diffusion Policies with Projective Geometric Algebra for Efficient Robot Manipulation Learning](https://mlsanity.com/paper/2507.05695/) (2025)
- [Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schr"odinger Bridges](https://mlsanity.com/paper/2506.02489/) (2025)
- [Discovering Phase Space Structure in Learned Hamiltonian Systems](https://mlsanity.com/paper/2509.23003/) (2025)
- [Neural Field Thermal Tomography: A Differentiable Physics Framework for Non-Destructive Evaluation](https://mlsanity.com/paper/2603.11045/) (2026)
- [EquiDexFlow: Contact-Grounded SE(3)-Equivariant Dexterous Grasp Generative Flows](https://mlsanity.com/paper/2606.12728/) (2026)
- [Local-Canonicalization Equivariant Graph Neural Networks for Sample-Efficient and Generalizable Swarm Robot Control](https://mlsanity.com/paper/2509.14431/) (2025)
- [NDPP-Grasp: Non-Differentiable Physical Plausibility Constraint-Guided Task-Oriented Dexterous Grasp Generation](https://mlsanity.com/paper/2606.02432/) (2026)

## Abstract (arXiv)

We propose GAGrasp, a novel framework for dexterous grasp generation that leverages geometric algebra representations to enforce equivariance to SE(3) transformations. By encoding the SE(3) symmetry constraint directly into the architecture, our method improves data and parameter efficiency while enabling robust grasp generation across diverse object poses. Additionally, we incorporate a differentiable physics-informed refinement layer, which ensures that generated grasps are physically plausible and stable. Extensive experiments demonstrate the model's superior performance in generalization, stability, and adaptability compared to existing methods. Additional details at https://gagrasp.github.io/