# Geometric Action Model for Robot Policy Learning

arXiv: https://arxiv.org/abs/2606.17046 · HTML: https://mlsanity.com/paper/2606.17046/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Embodied and robot world models, one of 11 directions in World models.
- Builds on 45 of its 55 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)
- Vision-language-action models / [3D and spatial-aware VLA](https://mlsanity.com/vla/3d-and-spatial-aware-vla/)

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

- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [Open X-Embodiment: Robotic Learning Datasets and RT-X Models](https://mlsanity.com/paper/2310.08864/) (2023)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [World Action Models are Zero-shot Policies](https://mlsanity.com/paper/2602.15922/) (2026)
- [UniVLA: Learning to Act Anywhere with Task-centric Latent Actions](https://mlsanity.com/paper/2505.06111/) (2025)
- [RoboCasa: Large-Scale Simulation of Everyday Tasks for Generalist Robots](https://mlsanity.com/paper/2406.02523/) (2024)
- [DINO-WM: World Models on Pre-trained Visual Features enable Zero-shot Planning](https://mlsanity.com/paper/2411.04983/) (2024)
- [WorldVLA: Towards Autoregressive Action World Model](https://mlsanity.com/paper/2506.21539/) (2025)
- [Fast-WAM: Do World Action Models Need Test-time Future Imagination?](https://mlsanity.com/paper/2603.16666/) (2026)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [MapAnything: Universal Feed-Forward Metric 3D Reconstruction](https://mlsanity.com/paper/2509.13414/) (2025)
- [LIBERO-Plus: In-depth Robustness Analysis of Vision-Language-Action Models](https://mlsanity.com/paper/2510.13626/) (2025)
- [Cosmos Policy: Fine-Tuning Video Models for Visuomotor Control and Planning](https://mlsanity.com/paper/2601.16163/) (2026)
- [Hi Robot: Open-Ended Instruction Following with Hierarchical Vision-Language-Action Models](https://mlsanity.com/paper/2502.19417/) (2025)
- [mimic-video: Video-Action Models for Generalizable Robot Control Beyond VLAs](https://mlsanity.com/paper/2512.15692/) (2025)
- [Interactive Post-Training for Vision-Language-Action Models](https://mlsanity.com/paper/2505.17016/) (2025)
- [Spatial Forcing: Implicit Spatial Representation Alignment for Vision-language-action Model](https://mlsanity.com/paper/2510.12276/) (2025)
- [NORA: A Small Open-Sourced Generalist Vision Language Action Model for Embodied Tasks](https://mlsanity.com/paper/2504.19854/) (2025)
- [3D Diffusion Policy: Generalizable Visuomotor Policy Learning via Simple 3D Representations](https://mlsanity.com/paper/2403.03954/) (2024)
- [FLARE: Robot Learning with Implicit World Modeling](https://mlsanity.com/paper/2505.15659/) (2025)

## Built on by (most cited first, 11 of 11)

- [GIFT: Guided Intermediate Feature Training via Action-Oriented Structural Supervision for Robotic Manipulation](https://mlsanity.com/paper/2609.04193/) (2026)
- [Rethinking Representations for World-Action Modeling](https://mlsanity.com/paper/2609.38163/) (2026)
- [Ontology-Grounded World Models for Failure Diagnosis and Closed-Loop Repair in Physical AI Systems](https://mlsanity.com/paper/2608.13901/) (2026)
- [WorldToken: Time-First Sequence Modeling for Robotic Imitation Learning](https://mlsanity.com/paper/2608.22591/) (2026)
- [GeoLAM: Learning Geometry-Grounded Latent Actions from Unlabeled Human Videos](https://mlsanity.com/paper/2609.17099/) (2026)
- [Acting in Meters: Learning Metric Interactions for Precise Robotic Manipulation](https://mlsanity.com/paper/2609.18243/) (2026)
- [JAMB: Joint Action-Motion Diffusion for Bimanual Manipulation](https://mlsanity.com/paper/2609.25322/) (2026)
- [SLIP-VLA: Single-Step Latent Imagination for Policy Learning in Vision-Language-Action Models](https://mlsanity.com/paper/2609.33575/) (2026)
- [Quantile Head for Vision-Language-Action Models](https://mlsanity.com/paper/2609.34061/) (2026)
- [PointWAM: 3D World Action Modeling for Dexterous Robotic Manipulation](https://mlsanity.com/paper/2610.02840/) (2026)
- [WARP-VLA: Wrist-Camera Adaptation for View-Robust Policy Execution in Vision-Language-Action Models](https://mlsanity.com/paper/2610.11508/) (2026)

## Abstract (arXiv)

Generalist robot policies must follow user instructions while reasoning about how objects, cameras, and robot actions interact in the 3D physical world. Recent vision-language-action models (VLAs) and video world-action models (WAMs) inherit strong semantic or temporal priors from large-scale foundation models, but they still operate primarily on 2D image frames or 2D-derived latent spaces, leaving implicit the 3D geometry required for contact-rich manipulation. We propose the Geometric Action Model (GAM), a language-conditioned manipulation policy that directly repurposes a pretrained geometric foundation model (GFM) as a shared substrate for perception, temporal prediction, and action decoding. GAM splits the GFM at an intermediate layer: the shallow layers serve as an observation encoder, and a causal future predictor inserted at the split layer forecasts future latent tokens conditioned on language, proprioception, and action history. The predicted future tokens are then routed through the remaining GFM blocks for feature propagation and decoding, allowing a single backbone to produce both future geometry and actions. This design equips the GFM with language-conditioned temporal world modeling through minimal architectural modification while preserving its rich geometric priors. Across a broad suite of simulation and real-robot manipulation benchmarks, GAM is more accurate, more robust, faster, and lighter than current foundation-model-scale baselines.