# GeoPredict: Leveraging Predictive Kinematics and 3D Gaussian Geometry for Precise VLA Manipulation

arXiv: https://arxiv.org/abs/2512.16811 · HTML: https://mlsanity.com/paper/2512.16811/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in 3D and spatial-aware VLA, one of 13 directions in Vision-language-action models.
- Builds on 50 of its 55 references that are in the map.
- First posted on arXiv 18 Dec 2025.

## 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, 30 of 50)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Ego4D: Around the World in 3,000 Hours of Egocentric Video](https://mlsanity.com/paper/2110.07058/) (2021)
- [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)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Mastering Atari with Discrete World Models](https://mlsanity.com/paper/2010.02193/) (2020)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [PaliGemma: A versatile 3B VLM for transfer](https://mlsanity.com/paper/2407.07726/) (2024)
- [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)
- [TD-MPC2: Scalable, Robust World Models for Continuous Control](https://mlsanity.com/paper/2310.16828/) (2023)
- [Point-NeRF: Point-based Neural Radiance Fields](https://mlsanity.com/paper/2201.08845/) (2022)
- [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)
- [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)
- [WorldVLA: Towards Autoregressive Action World Model](https://mlsanity.com/paper/2506.21539/) (2025)
- [Unleashing Large-Scale Video Generative Pre-training for Visual Robot Manipulation](https://mlsanity.com/paper/2312.13139/) (2023)
- [Vision-Language Foundation Models as Effective Robot Imitators](https://mlsanity.com/paper/2311.01378/) (2023)
- [Transformers are Sample-Efficient World Models](https://mlsanity.com/paper/2209.00588/) (2022)
- [TraceVLA: Visual Trace Prompting Enhances Spatial-Temporal Awareness for Generalist Robotic Policies](https://mlsanity.com/paper/2412.10345/) (2024)
- [Video Prediction Policy: A Generalist Robot Policy with Predictive Visual Representations](https://mlsanity.com/paper/2412.14803/) (2024)

## Built on by (most cited first, 17 of 17)

- [STARRY: Spatial-Temporal Action-Centric World Modeling for Robotic Manipulation](https://mlsanity.com/paper/2604.26848/) (2026)
- [GuidedVLA: Specifying Task-Relevant Factors via Plug-and-Play Action Attention Specialization](https://mlsanity.com/paper/2605.12369/) (2026)
- [Track4Action: Distilling World-Centric 3D Tracker into Vision-Language-Action Policies](https://mlsanity.com/paper/2608.03727/) (2026)
- [GaussianDream: A Feed-Forward 3D Gaussian World Model for Robotic Manipulation](https://mlsanity.com/paper/2605.20752/) (2026)
- [FoMoVLA: Bridging Visual Foresight and Motion Guidance for Vision-Language-Action Models](https://mlsanity.com/paper/2607.14739/) (2026)
- [ELAN4D: Embodiment-Centric 4D Supervision for Vision-Language-Action Models via Plug-and-Play Adaptation](https://mlsanity.com/paper/2605.30484/) (2026)
- [3DThinkVLA: Endowing Vision-Language-Action Models with Latent 3D Priors via 3D-Thinking-Guided Co-training](https://mlsanity.com/paper/2606.04436/) (2026)
- [GeoProp: Grounding Robot State in Vision for Generalist Manipulation](https://mlsanity.com/paper/2607.07101/) (2026)
- [Breaking Structural Isolation: Scalable Graph Clustering via Community-Aware Sampling and Structural Entropy](https://mlsanity.com/paper/2607.05469/) (2026)
- [GaussianDream++: Efficient 3D Gaussian World Modeling for Robotic Manipulation](https://mlsanity.com/paper/2608.25659/) (2026)
- [Monocular Depth Estimation from a Single Image: Progress and Opportunities](https://mlsanity.com/paper/2609.01172/) (2026)
- [StrataVLA: Hierarchical and Efficient 3D Geometric Grounding for Vision-Language-Action Models](https://mlsanity.com/paper/2609.26071/) (2026)
- [SLIP-VLA: Single-Step Latent Imagination for Policy Learning in Vision-Language-Action Models](https://mlsanity.com/paper/2609.33575/) (2026)
- [Spatial Grafting: Grounding 3D Features for Flow-Matching Robot Policies](https://mlsanity.com/paper/2609.35249/) (2026)
- [ForeAct3D: Policy-Grounded Future World Modeling for VLA Policies](https://mlsanity.com/paper/2610.04607/) (2026)
- [Triggering Generalist Reasoning via Predictive Uncertainty for Dual-System VLA](https://mlsanity.com/paper/2610.05025/) (2026)
- [VersaCamVLA: Camera-Configurable VLA Policies for Robotic Manipulation](https://mlsanity.com/paper/2610.12451/) (2026)

## Abstract (arXiv)

Vision-Language-Action (VLA) models achieve strong generalization in robotic manipulation but remain largely reactive and 2D-centric, making them unreliable in tasks that require precise 3D reasoning. We propose GeoPredict, a geometry-aware VLA framework that augments a continuous-action policy with predictive kinematic and geometric priors. GeoPredict introduces a trajectory-level module that encodes motion history and predicts multi-step 3D keypoint trajectories of robot arms, and a predictive 3D Gaussian geometry module that forecasts workspace geometry with track-guided refinement along future keypoint trajectories. These predictive modules serve exclusively as training-time supervision through depth-based rendering, while inference requires only lightweight additional query tokens without invoking any 3D decoding. Experiments on RoboCasa Human-50, LIBERO, and real-world manipulation tasks show that GeoPredict consistently outperforms strong VLA baselines, especially in geometry-intensive and spatially demanding scenarios.