# Spatial Grafting: Grounding 3D Features for Flow-Matching Robot Policies

arXiv: https://arxiv.org/abs/2609.35249 · HTML: https://mlsanity.com/paper/2609.35249/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Embodied and robot world models, one of 11 directions in World models.
- Builds on 39 of its 43 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- World models / [Embodied and robot world models](https://mlsanity.com/wm/embodied-and-robot-world-models/)
- Vision-language-action models / [3D and spatial-aware VLA](https://mlsanity.com/vla/3d-and-spatial-aware-vla/)
- 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 39)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer](https://mlsanity.com/paper/1907.01341/) (2019)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [Depth Anything V2](https://mlsanity.com/paper/2406.09414/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [Depth Anything: Unleashing the Power of Large-Scale Unlabeled Data](https://mlsanity.com/paper/2401.10891/) (2024)
- [Grounding Image Matching in 3D with MASt3R](https://mlsanity.com/paper/2406.09756/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [RoboTwin 2.0: A Scalable Data Generator and Benchmark with Strong Domain Randomization for Robust Bimanual Robotic Manipulation](https://mlsanity.com/paper/2506.18088/) (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)
- [X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Model](https://mlsanity.com/paper/2510.10274/) (2025)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Motus: A Unified Latent Action World Model](https://mlsanity.com/paper/2512.13030/) (2025)
- [MolmoAct: Action Reasoning Models that can Reason in Space](https://mlsanity.com/paper/2508.07917/) (2025)
- [Act3D: 3D Feature Field Transformers for Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2306.17817/) (2023)
- [Spatial Forcing: Implicit Spatial Representation Alignment for Vision-language-action Model](https://mlsanity.com/paper/2510.12276/) (2025)
- [PointVLA: Injecting the 3D World into Vision-Language-Action Models](https://mlsanity.com/paper/2503.07511/) (2025)
- [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)
- [DepthVLA: Enhancing Vision-Language-Action Models with Depth-Aware Spatial Reasoning](https://mlsanity.com/paper/2510.13375/) (2025)
- [GWM: Towards Scalable Gaussian World Models for Robotic Manipulation](https://mlsanity.com/paper/2508.17600/) (2025)

## Abstract (arXiv)

Pretrained robot manipulation policies such as vision-language-action models (VLAs) or world-action models (WAMs) leave interaction-relevant metric geometry implicit. Recent breakthroughs in spatial reconstruction can supply the necessary geometry reliably, but their features describe local shape without stating where it lies with respect to the robot. How best to deliver these features to a pretrained policy remains unresolved. We propose Spatial Grafting, a versatile, lightweight spatial module that binds frozen reconstruction features to metric, robot-relative geometry. Spatial Grafting constructs metric-grounded spatial tokens and injects them into the flow-matching action expert through cross-attention, without modifying the host's perceptual pathway, so the host retains the full benefit of its pretraining. We evaluate it more broadly than any geometry-aware policy we compare against: one graft architecture, with no per-host redesign, on two VLAs and two WAMs, across four simulation benchmarks that span short-horizon manipulation, visual robustness, clutter and long-horizon mobile manipulation, and on three real-robot platforms with single- and dual-arm configurations. On RoboTwin 2.0, a dual-arm manipulation benchmark, the graft improves every host across VLAs and WAMs. Grafted π0.5 gains 11.3% and 15.6% on clean and randomized scenes, reaching 94.0% and 92.4%, above the strongest published 3D-conditioned policy, WAM4D (93.8% and 89.9%). The margin widens as the horizon lengthens: on tasks from BEHAVIOR-1K, a dual-arm mobile manipulation challenge scored by average task progress, it surpasses the 2025 challenge winner on five of six tasks,by up to 0.47 Q-score, and exceeds a map-conditioned spatial policy on average across the three tasks both report.