# CoFL: Continuous Flow Fields for Language-Conditioned Navigation

arXiv: https://arxiv.org/abs/2603.02854 · HTML: https://mlsanity.com/paper/2603.02854/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 51 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Sigmoid Loss for Language Image Pre-Training](https://mlsanity.com/paper/2303.15343/) (2023)
- [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)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [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)
- [PaLM-E: An Embodied Multimodal Language Model](https://mlsanity.com/paper/2303.03378/) (2023)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [SigLIP 2: Multilingual Vision-Language Encoders with Improved Semantic Understanding, Localization, and Dense Features](https://mlsanity.com/paper/2502.14786/) (2025)
- [Lift, Splat, Shoot: Encoding Images From Arbitrary Camera Rigs by Implicitly Unprojecting to 3D](https://mlsanity.com/paper/2008.05711/) (2020)
- [Vision-and-Language Navigation: Interpreting visually-grounded navigation instructions in real environments](https://mlsanity.com/paper/1711.07280/) (2017)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [LM-Nav: Robotic Navigation with Large Pre-Trained Models of Language, Vision, and Action](https://mlsanity.com/paper/2207.04429/) (2022)
- [π*0.6: a VLA That Learns From Experience](https://mlsanity.com/paper/2511.14759/) (2025)
- [A Recurrent Vision-and-Language BERT for Navigation](https://mlsanity.com/paper/2011.13922/) (2020)
- [History Aware Multimodal Transformer for Vision-and-Language Navigation](https://mlsanity.com/paper/2110.13309/) (2021)
- [CoWs on Pasture: Baselines and Benchmarks for Language-Driven Zero-Shot Object Navigation](https://mlsanity.com/paper/2203.10421/) (2022)
- [MapGPT: Map-Guided Prompting with Adaptive Path Planning for Vision-and-Language Navigation](https://mlsanity.com/paper/2401.07314/) (2024)

## Built on by (most cited first, 2 of 2)

- [CoFL-S: Spatially Queryable Sector Flow Fields for Local Language-Conditioned Navigation](https://mlsanity.com/paper/2607.02222/) (2026)
- [UDAV: Uncertainty-Driven Adaptive VLM Waypoint Planner](https://mlsanity.com/paper/2609.16368/) (2026)

## Abstract (arXiv)

Existing language-conditioned navigation systems typically rely on modular pipelines or trajectory generators, but the latter use each scene--instruction annotation mainly to supervise one start-conditioned rollout. To address these limitations, we present CoFL, an end-to-end policy that maps a bird's-eye view (BEV) observation and a language instruction to a continuous flow field for navigation. CoFL reformulates navigation as workspace-conditioned field learning rather than start-conditioned trajectory prediction: it learns local motion vectors at arbitrary BEV locations, turning each scene--instruction annotation into dense spatial control supervision. Trajectories are generated from any start by numerical integration of the predicted field, enabling simple real-time rollout and closed-loop recovery. To enable large-scale training and evaluation, we build a dataset of over 500k BEV image--instruction pairs, each procedurally annotated with a flow field and a trajectory derived from semantic maps built on Matterport3D and ScanNet. Evaluating on strictly unseen scenes, CoFL significantly outperforms modular Vision-Language Model (VLM)-based planners and trajectory generation policies in both navigation precision and safety, while maintaining real-time inference. Finally, we deploy CoFL zero-shot in real-world experiments with BEV observations across multiple layouts, maintaining feasible closed-loop control and a high success rate.