# GAF: Gaussian Action Field as a 4D Representation for Dynamic World Modeling in Robotic Manipulation

arXiv: https://arxiv.org/abs/2506.14135 · HTML: https://mlsanity.com/paper/2506.14135/

## 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 44 of its 49 references that are in the map.
- First posted on arXiv 17 Jun 2025.

## 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 44)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [ViLBERT: Pretraining Task-Agnostic Visiolinguistic Representations for Vision-and-Language Tasks](https://mlsanity.com/paper/1908.02265/) (2019)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Vision Transformers for Dense Prediction](https://mlsanity.com/paper/2103.13413/) (2021)
- [Dream to Control: Learning Behaviors by Latent Imagination](https://mlsanity.com/paper/1912.01603/) (2019)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Mastering Diverse Domains through World Models](https://mlsanity.com/paper/2301.04104/) (2023)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [Recurrent World Models Facilitate Policy Evolution](https://mlsanity.com/paper/1809.01999/) (2018)
- [RLBench: The Robot Learning Benchmark & Learning Environment](https://mlsanity.com/paper/1909.12271/) (2019)
- [Perceiver-Actor: A Multi-Task Transformer for Robotic Manipulation](https://mlsanity.com/paper/2209.05451/) (2022)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [3D-VLA: A 3D Vision-Language-Action Generative World Model](https://mlsanity.com/paper/2403.09631/) (2024)
- [Zero-Shot Robotic Manipulation with Pretrained Image-Editing Diffusion Models](https://mlsanity.com/paper/2310.10639/) (2023)
- [No Pose, No Problem: Surprisingly Simple 3D Gaussian Splats from Sparse Unposed Images](https://mlsanity.com/paper/2410.24207/) (2024)
- [RVT: Robotic View Transformer for 3D Object Manipulation](https://mlsanity.com/paper/2306.14896/) (2023)
- [Masked World Models for Visual Control](https://mlsanity.com/paper/2206.14244/) (2022)
- [Model-Based Imitation Learning for Urban Driving](https://mlsanity.com/paper/2210.07729/) (2022)
- [Structured World Models from Human Videos](https://mlsanity.com/paper/2308.10901/) (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)
- [ManiGaussian: Dynamic Gaussian Splatting for Multi-task Robotic Manipulation](https://mlsanity.com/paper/2403.08321/) (2024)

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

- [Agentic World Modeling: Foundations, Capabilities, Laws, and Beyond](https://mlsanity.com/paper/2604.22748/) (2026)
- [Feed-Forward 3D Scene Modeling: A Problem-Driven Perspective](https://mlsanity.com/paper/2604.14025/) (2026)
- [Learning Visual Feature-Based World Models via Residual Latent Action](https://mlsanity.com/paper/2605.07079/) (2026)
- [Structured 4D Latent Predictive Model for Robot Planning](https://mlsanity.com/paper/2607.01166/) (2026)
- [3D Generation for Embodied AI and Robotic Simulation: A Survey](https://mlsanity.com/paper/2604.26509/) (2026)
- [Learning Action-Conditional and Object-Centric Gaussian Splatting World Models for Rigid Objects](https://mlsanity.com/paper/2606.01950/) (2026)
- [World Models for Embodied Intelligence: From Plausible to Controllable to Actionable](https://mlsanity.com/paper/2609.16697/) (2026)
- [VistaVLA: Geometry- and Semantic-Aware 3D Gaussian-Grounded VLA for Robotic Manipulation](https://mlsanity.com/paper/2607.12356/) (2026)
- [Quo Vadis, World Modeling?](https://mlsanity.com/paper/2608.02713/) (2026)
- [From Generation to Simulation: How Far Are World Models from Being True Simulators?](https://mlsanity.com/paper/2608.23070/) (2026)
- [4DGS-JEPA: Temporally Compositional Joint-Embedding Prediction for Dynamic Gaussian Splatting](https://mlsanity.com/paper/2609.25036/) (2026)

## Abstract (arXiv)

Accurate scene perception is critical for vision-based robotic manipulation. Existing approaches typically follow either a Vision-to-Action (V-A) paradigm, predicting actions directly from visual inputs, or a Vision-to-3D-to-Action (V-3D-A) paradigm, leveraging intermediate 3D representations. However, these methods often struggle with action inaccuracies due to the complexity and dynamic nature of manipulation scenes. In this paper, we adopt a V-4D-A framework that enables direct action reasoning from motion-aware 4D representations via a Gaussian Action Field (GAF). GAF extends 3D Gaussian Splatting (3DGS) by incorporating learnable motion attributes, allowing 4D modeling of dynamic scenes and manipulation actions. To learn time-varying scene geometry and action-aware robot motion, GAF provides three interrelated outputs: reconstruction of the current scene, prediction of future frames, and estimation of init action via Gaussian motion. Furthermore, we employ an action-vision-aligned denoising framework, conditioned on a unified representation that combines the init action and the Gaussian perception, both generated by the GAF, to further obtain more precise actions. Extensive experiments demonstrate significant improvements, with GAF achieving +11.5385 dB PSNR, +0.3864 SSIM and -0.5574 LPIPS improvements in reconstruction quality, while boosting the average +7.3% success rate in robotic manipulation tasks over state-of-the-art methods.