# GST-VLA: Structured Gaussian Spatial Tokens for 3D Depth-Aware Vision-Language-Action Models

arXiv: https://arxiv.org/abs/2603.09079 · HTML: https://mlsanity.com/paper/2603.09079/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D and spatial-aware VLA, one of 13 directions in Vision-language-action models.
- Builds on 16 of its 17 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Placed in

- Vision-language-action models / [3D and spatial-aware VLA](https://mlsanity.com/vla/3d-and-spatial-aware-vla/)

## Builds on (most cited first, 16 of 16)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [Hypersim: A Photorealistic Synthetic Dataset for Holistic Indoor Scene Understanding](https://mlsanity.com/paper/2011.02523/) (2020)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [Evaluating Real-World Robot Manipulation Policies in Simulation](https://mlsanity.com/paper/2405.05941/) (2024)
- [ARKitScenes: A Diverse Real-World Dataset For 3D Indoor Scene Understanding Using Mobile RGB-D Data](https://mlsanity.com/paper/2111.08897/) (2021)
- [CoT-VLA: Visual Chain-of-Thought Reasoning for Vision-Language-Action Models](https://mlsanity.com/paper/2503.22020/) (2025)
- [CogACT: A Foundational Vision-Language-Action Model for Synergizing Cognition and Action in Robotic Manipulation](https://mlsanity.com/paper/2411.19650/) (2024)
- [Robotic Control via Embodied Chain-of-Thought Reasoning](https://mlsanity.com/paper/2407.08693/) (2024)
- [3D-VLA: A 3D Vision-Language-Action Generative World Model](https://mlsanity.com/paper/2403.09631/) (2024)
- [HybridVLA: Collaborative Diffusion and Autoregression in a Unified Vision-Language-Action Model](https://mlsanity.com/paper/2503.10631/) (2025)
- [GaussTR: Foundation Model-Aligned Gaussian Transformer for Self-Supervised 3D Spatial Understanding](https://mlsanity.com/paper/2412.13193/) (2024)
- [DepthVLA: Enhancing Vision-Language-Action Models with Depth-Aware Spatial Reasoning](https://mlsanity.com/paper/2510.13375/) (2025)
- [GPSToken: Gaussian Parameterized Spatially-adaptive Tokenization for Image Representation and Generation](https://mlsanity.com/paper/2509.01109/) (2025)

## Abstract (arXiv)

VLA models encode visual observations as 2D patch tokens with no intrinsic geometric structure. We introduce GST-VLA with two contributions. First, the Gaussian Spatial Tokenizer (GST) converts frozen dense depth and frozen semantic patch features into Ng=128 anisotropic 3D Gaussian primitives, each parameterized by a metric residual mean μ ∈ ℝ3, log-scale covariance log σ ∈ ℝ3, and learned opacity α ∈ (0,1). The covariance eigenstructure encodes local surface orientation, and opacity provides per-primitive geometric confidence, both inaccessible from scalar depth. Spatial attention pooling with learned queries concentrates the fixed token budget on geometrically salient regions rather than distributing uniformly. Second, 3D Depth-Aware Chain-of-Thought (DA-CoT) reasoning supervises four structured intermediate spatial thoughts, covering 3D object grounding, grasp affordance contact geometry, pairwise metric distances, and coarse SE(3) waypoints, as explicit generation targets in the training loss. A cross-attention sublayer at every VLM transformer block provides direct access to the raw 256-primitive Gaussian field during DA-CoT generation. A 300M-parameter flow-matching action expert with mixture-of-experts feedforward sublayers decodes 7-DoF delta action chunks via conditional ODE integration, conditioned on both VLM hidden states and DA-CoT outputs through dual cross-attention. Trained with composite Lflow + LCoT + Ldepth across three progressive stages, GST-VLA achieves 96.4% on LIBERO (+2.0%), and 80.2% on SimplerEnv (+5.4%). Ablations isolate the contribution of each GST component, each DA-CoT thought, and each training stage, confirming independent and synergistic gains concentrated on precision demanding tasks.