# Geometry-Aware Motion Latents for Learning Robust Manipulation Policies

arXiv: https://arxiv.org/abs/2607.04714 · HTML: https://mlsanity.com/paper/2607.04714/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [CALVIN: A Benchmark for Language-Conditioned Policy Learning for Long-Horizon Robot Manipulation Tasks](https://mlsanity.com/paper/2112.03227/) (2021)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [BC-Z: Zero-Shot Task Generalization with Robotic Imitation Learning](https://mlsanity.com/paper/2202.02005/) (2022)
- [Mobile ALOHA: Learning Bimanual Mobile Manipulation with Low-Cost Whole-Body Teleoperation](https://mlsanity.com/paper/2401.02117/) (2024)
- [Unleashing Large-Scale Video Generative Pre-training for Visual Robot Manipulation](https://mlsanity.com/paper/2312.13139/) (2023)
- [Latent Action Pretraining from Videos](https://mlsanity.com/paper/2410.11758/) (2024)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Zero-Shot Robotic Manipulation with Pretrained Image-Editing Diffusion Models](https://mlsanity.com/paper/2310.10639/) (2023)
- [RVT: Robotic View Transformer for 3D Object Manipulation](https://mlsanity.com/paper/2306.14896/) (2023)
- [Act3D: 3D Feature Field Transformers for Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2306.17817/) (2023)
- [RVT-2: Learning Precise Manipulation from Few Demonstrations](https://mlsanity.com/paper/2406.08545/) (2024)
- [Coarse-to-Fine Q-attention: Efficient Learning for Visual Robotic Manipulation via Discretisation](https://mlsanity.com/paper/2106.12534/) (2021)
- [3D Diffusion Policy: Generalizable Visuomotor Policy Learning via Simple 3D Representations](https://mlsanity.com/paper/2403.03954/) (2024)
- [ManiGaussian: Dynamic Gaussian Splatting for Multi-task Robotic Manipulation](https://mlsanity.com/paper/2403.08321/) (2024)
- [Imitating Latent Policies from Observation](https://mlsanity.com/paper/1805.07914/) (2018)
- [GNFactor: Multi-Task Real Robot Learning with Generalizable Neural Feature Fields](https://mlsanity.com/paper/2308.16891/) (2023)
- [Reducing the Barrier to Entry of Complex Robotic Software: a MoveIt! Case Study](https://mlsanity.com/paper/1404.3785/) (2014)
- [SkillDiffuser: Interpretable Hierarchical Planning via Skill Abstractions in Diffusion-Based Task Execution](https://mlsanity.com/paper/2312.11598/) (2023)
- [Closed-Loop Visuomotor Control with Generative Expectation for Robotic Manipulation](https://mlsanity.com/paper/2409.09016/) (2024)

## Abstract (arXiv)

Learning motion latents for robotic manipulation heavily relies on extracting motion patterns from visual sequences, yet effective action abstractions require understanding three-dimensional geometric transformations. Here, we introduce GeoMoLa (Geometry-Aware Motion Latents), which learns discrete motion latent codes by predicting how point clouds evolve during manipulation rather than reconstructing visual observations. This four-dimensional objective -- spatial geometry changing through time -- forces latent representations to encode actual physical motion rather than appearance patterns. GeoMoLa achieves state-of-the-art performance using only single-view RGB-D input, while existing methods require multi-view reconstruction, succeeding across diverse manipulation benchmarks. Our ablations reveal that geometric prediction is the key to driving performance, quantitatively validating that manipulation depends on spatial understanding. Furthermore, the learned codes exhibit effective motion abstraction: applying them to novel scenes produces physically consistent transformations regardless of visual context. Our real-world experiments also confirm this robustness capability, achieving robust manipulation with minimal demonstrations in cluttered environments where geometric reasoning determines success. Thus, we demonstrate that effective motion latents for robot control can better emerge from understanding motion through its three-dimensional effects rather than pixel-level patterns.