# Flow as Flow: Modeling Robot Velocity Fields as Probability Velocity Fields for Flow-Based Object Manipulation

arXiv: https://arxiv.org/abs/2606.23090 · HTML: https://mlsanity.com/paper/2606.23090/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 80 of its 85 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Placed in

- 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 80)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Ego4D: Around the World in 3,000 Hours of Egocentric Video](https://mlsanity.com/paper/2110.07058/) (2021)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Frozen in Time: A Joint Video and Image Encoder for End-to-End Retrieval](https://mlsanity.com/paper/2104.00650/) (2021)
- [The "something something" video database for learning and evaluating visual common sense](https://mlsanity.com/paper/1706.04261/) (2017)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [DROID: A Large-Scale In-The-Wild Robot Manipulation Dataset](https://mlsanity.com/paper/2403.12945/) (2024)
- [Scaling Egocentric Vision: The EPIC-KITCHENS Dataset](https://mlsanity.com/paper/1804.02748/) (2018)
- [R3M: A Universal Visual Representation for Robot Manipulation](https://mlsanity.com/paper/2203.12601/) (2022)
- [BridgeData V2: A Dataset for Robot Learning at Scale](https://mlsanity.com/paper/2308.12952/) (2023)
- [Learning Universal Policies via Text-Guided Video Generation](https://mlsanity.com/paper/2302.00111/) (2023)
- [CoTracker: It is Better to Track Together](https://mlsanity.com/paper/2307.07635/) (2023)
- [Ego-Exo4D: Understanding Skilled Human Activity from First- and Third-Person Perspectives](https://mlsanity.com/paper/2311.18259/) (2023)
- [UniVLA: Learning to Act Anywhere with Task-centric Latent Actions](https://mlsanity.com/paper/2505.06111/) (2025)
- [VIP: Towards Universal Visual Reward and Representation via Value-Implicit Pre-Training](https://mlsanity.com/paper/2210.00030/) (2022)
- [Latent Action Pretraining from Videos](https://mlsanity.com/paper/2410.11758/) (2024)
- [MERLOT: Multimodal Neural Script Knowledge Models](https://mlsanity.com/paper/2106.02636/) (2021)

## Built on by (most cited first, 1 of 1)

- [NarrativeFlow: Flow-Based Vision-Language-Action Model Using Robot Velocity Fields](https://mlsanity.com/paper/2610.00981/) (2026)

## Abstract (arXiv)

Cross-embodiment data have become central to training robotic foundation models. To leverage such heterogeneous data, we focus on flow-based object manipulation, where robot flows (robot velocity fields) serve as embodiment-agnostic motion representations. Previous studies do not formulate robot flows as dense velocity fields, but as displacements of sparse keypoints, even though dense velocity fields better match the continuous-time nature of motions. To address this, we propose Flow as Flow, a framework that models robot flows as probability flows based on a flow matching formulation. By naturally modeling such velocity fields within this formulation, our method achieves efficient and high-quality robot flow generation. Across standard benchmarks, our method outperforms representative baseline methods on standard metrics, while achieving approximately 24× faster generation than standard flow matching. Furthermore, through real-world experiments evaluating 9 methods with 260 trials per method across 13 manipulation tasks, we show that our method achieves a higher average success rate than the baseline methods.