# WAM4D: Fast 4D World Action Model via Spatial Register Tokens

arXiv: https://arxiv.org/abs/2606.14048 · HTML: https://mlsanity.com/paper/2606.14048/

## Key facts

- Cited by 15 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 70 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)

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

- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [Fast-WAM: Do World Action Models Need Test-time Future Imagination?](https://mlsanity.com/paper/2603.16666/) (2026)
- [Causal World Modeling for Robot Control](https://mlsanity.com/paper/2601.21998/) (2026)
- [π3: Permutation-Equivariant Visual Geometry Learning](https://mlsanity.com/paper/2507.13347/) (2025)
- [Motus: A Unified Latent Action World Model](https://mlsanity.com/paper/2512.13030/) (2025)
- [RoboDreamer: Learning Compositional World Models for Robot Imagination](https://mlsanity.com/paper/2404.12377/) (2024)
- [Seedance 2.0: Advancing Video Generation for World Complexity](https://mlsanity.com/paper/2604.14148/) (2026)
- [π0.7: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities](https://mlsanity.com/paper/2604.15483/) (2026)
- [Spatial Forcing: Implicit Spatial Representation Alignment for Vision-language-action Model](https://mlsanity.com/paper/2510.12276/) (2025)
- [ManiGaussian: Dynamic Gaussian Splatting for Multi-task Robotic Manipulation](https://mlsanity.com/paper/2403.08321/) (2024)
- [textitS3Gaussian: Self-Supervised Street Gaussians for Autonomous Driving](https://mlsanity.com/paper/2405.20323/) (2024)
- [TesserAct: Learning 4D Embodied World Models](https://mlsanity.com/paper/2504.20995/) (2025)
- [Manipulate-Anything: Automating Real-World Robots using Vision-Language Models](https://mlsanity.com/paper/2406.18915/) (2024)
- [Unified 4D World Action Modeling from Video Priors with Asynchronous Denoising](https://mlsanity.com/paper/2604.26694/) (2026)
- [GeoVLA: Empowering 3D Representations in Vision-Language-Action Models](https://mlsanity.com/paper/2508.09071/) (2025)
- [WoW: Towards a World omniscient World model Through Embodied Interaction](https://mlsanity.com/paper/2509.22642/) (2025)
- [Motubrain: An Advanced World Action Model for Robot Control](https://mlsanity.com/paper/2604.27792/) (2026)
- [World Action Models: The Next Frontier in Embodied AI](https://mlsanity.com/paper/2605.12090/) (2026)
- [NeoVerse: Enhancing 4D World Model with in-the-wild Monocular Videos](https://mlsanity.com/paper/2601.00393/) (2026)
- [Lyra 2.0: Explorable Generative 3D Worlds](https://mlsanity.com/paper/2604.13036/) (2026)
- [VLM4VLA: Revisiting Vision-Language-Models in Vision-Language-Action Models](https://mlsanity.com/paper/2601.03309/) (2026)

## Built on by (most cited first, 15 of 15)

- [Learning 4D Geometric Priors for Inference-Efficient World Action Models](https://mlsanity.com/paper/2607.05468/) (2026)
- [4D-WAM: Infusing Spatiotemporal Awareness into World Action Models through Trajectory Fields](https://mlsanity.com/paper/2608.08023/) (2026)
- [LD4WAM: Learning Latent Dynamics from Human Videos for World Action Models](https://mlsanity.com/paper/2608.22403/) (2026)
- [SUV: Future Scene Understanding as Video Generation for End-to-End Driving](https://mlsanity.com/paper/2608.03084/) (2026)
- [Modality-Autoregressive World-Action Models](https://mlsanity.com/paper/2609.17524/) (2026)
- [Rethinking Representations for World-Action Modeling](https://mlsanity.com/paper/2609.38163/) (2026)
- [Breaking Structural Isolation: Scalable Graph Clustering via Community-Aware Sampling and Structural Entropy](https://mlsanity.com/paper/2607.05469/) (2026)
- [Temporal Forcing: 4D Representation Alignment for Vision-Language-Action Models](https://mlsanity.com/paper/2608.30643/) (2026)
- [Learning to Use Imagination: Progress-Conditioned Future Utilization for World Action Models](https://mlsanity.com/paper/2609.06578/) (2026)
- [Acting in Meters: Learning Metric Interactions for Precise Robotic Manipulation](https://mlsanity.com/paper/2609.18243/) (2026)
- [Spatial Grafting: Grounding 3D Features for Flow-Matching Robot Policies](https://mlsanity.com/paper/2609.35249/) (2026)
- [MVG-WAM: Multiple View Geometry-Aware World-Action Modeling for Robotic Manipulation](https://mlsanity.com/paper/2609.37793/) (2026)
- [XGenAct: Geometry-Enhanced World Action Models through Cross-Task Generation](https://mlsanity.com/paper/2610.03516/) (2026)
- [SimForcing: Distilling Simulation Motion Priors into Real-Domain Robot World Models](https://mlsanity.com/paper/2610.06598/) (2026)
- [Thinker-WM: A Unified World Model with Shared Multimodal Representations for Embodied Intelligence](https://mlsanity.com/paper/2610.18447/) (2026)

## Abstract (arXiv)

World action models (WAMs) have recently shown promise in jointly modeling future observations and executable robot actions. However, most existing WAMs still operate in 2D video or latent spaces, where visually plausible rollouts miss the 3D spatial constraints and occluded contact geometry required for precise manipulation. While geometric foundation models offer strong priors for recovering dense 3D structure and motion from visual observations, forcing WAMs to predict the dense 4D representation introduces costly geometric decoding and slows down causal action generation. To address the trade-off, we present WAM4D, a fast 4D world action model that uses lightweight spatial register tokens as training-time future-depth readouts to transfer pretrained geometric priors into a causal video-action transformer, then removes the register branch for lightweight action inference. To prevent non-causal shortcuts, we further design causal mixture attention for the Mixture-of-Transformers (MoT) WAM backbone, defining modality-specific visibility among video, action, and geometry tokens. Comprehensive experiments on RoboTwin 2.0 and challenging real-world manipulation tasks show that WAM4D improves spatial consistency and achieves competitive action prediction while maintaining efficient inference.