# Spatially Aware World Action Model via Geometric Latent Diffusion arXiv: https://arxiv.org/abs/2609.02531 · HTML: https://mlsanity.com/paper/2609.02531/ ## Key facts - Cited by 5 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 46 of its 50 references that are in the map. - First posted on arXiv 2 Sep 2026. ## Placed in - World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/) - Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/) ## Builds on (most cited first, 30 of 46) - [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018) - [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023) - [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022) - [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) - [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024) - [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023) - [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018) - [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) - [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018) - [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025) - [Learning Universal Policies via Text-Guided Video Generation](https://mlsanity.com/paper/2302.00111/) (2023) - [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) - [Fast-WAM: Do World Action Models Need Test-time Future Imagination?](https://mlsanity.com/paper/2603.16666/) (2026) - [3D-VLA: A 3D Vision-Language-Action Generative World Model](https://mlsanity.com/paper/2403.09631/) (2024) - [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) - [Motus: A Unified Latent Action World Model](https://mlsanity.com/paper/2512.13030/) (2025) - [Unified World Models: Coupling Video and Action Diffusion for Pretraining on Large Robotic Datasets](https://mlsanity.com/paper/2504.02792/) (2025) - [Unified Video Action Model](https://mlsanity.com/paper/2503.00200/) (2025) - [mimic-video: Video-Action Models for Generalizable Robot Control Beyond VLAs](https://mlsanity.com/paper/2512.15692/) (2025) - [π0.7: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities](https://mlsanity.com/paper/2604.15483/) (2026) - [Interactive Post-Training for Vision-Language-Action Models](https://mlsanity.com/paper/2505.17016/) (2025) - [FLARE: Robot Learning with Implicit World Modeling](https://mlsanity.com/paper/2505.15659/) (2025) - [PointVLA: Injecting the 3D World into Vision-Language-Action Models](https://mlsanity.com/paper/2503.07511/) (2025) - [ABot-M0: VLA Foundation Model for Robotic Manipulation with Action Manifold Learning](https://mlsanity.com/paper/2602.11236/) (2026) ## Built on by (most cited first, 5 of 5) - [FOCAL-VLA: Subtask-Guided Geometry Distillation and Implicit World Modeling for Vision-Language-Action Models](https://mlsanity.com/paper/2609.21228/) (2026) - [From World Models to World Action Models: Rethinking Next-State Prediction](https://mlsanity.com/paper/2609.34414/) (2026) - [XGenAct: Geometry-Enhanced World Action Models through Cross-Task Generation](https://mlsanity.com/paper/2610.03516/) (2026) - [OpenWAM: An Open Framework for Composable World-Action Models](https://mlsanity.com/paper/2610.07922/) (2026) - [SmolWAM: A Latent World-Action Model for Robotic Manipulation on Edge Devices](https://mlsanity.com/paper/2610.13740/) (2026) ## Abstract (arXiv) World Action Models (WAMs) leverage the capabilities of large-scale pretrained video diffusion models to jointly predict future observations and actions, inheriting rich visual and physical priors from internet-scale video. This has made them a promising paradigm for robot policy learning, yet the prevailing models operate exclusively on RGB observations and do not leverage 3D information. To bridge this gap, we introduce a Spatially Aware World Action Model (SA-WAM), which repurposes a pretrained video model for joint action, RGB, and depth prediction, enabling 3D-aware world modeling and action prediction within a single diffusion backbone. We use a nonlinear encoding that maps the unbounded depth signal into the bounded input domain expected by the frozen VAE tokenizer. This allows us to reuse the tokenizer without 3D-specific fine-tuning, incorporating geometric information without sacrificing the pretrained priors. SA-WAM achieves state-of-the-art results on the RoboCasa and LIBERO-Plus benchmarks, while simultaneously improving future-state predictions. Furthermore, SA-WAM outperforms strong baselines in real-world evaluation using a UR5 robotic arm, with strong gains in randomized environments. We analyze the correlation between world model prediction quality and rollout success, providing insights into WAM performance and avenues for its improvement.