# CoLA-Flow Policy: Temporally Coherent Imitation Learning via Continuous Latent Action Flow Matching for Robotic Manipulation

arXiv: https://arxiv.org/abs/2601.23087 · HTML: https://mlsanity.com/paper/2601.23087/

## Key facts

- Cited by 2 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 33 of its 43 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [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)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learning](https://mlsanity.com/paper/1910.10897/) (2019)
- [Genie: Generative Interactive Environments](https://mlsanity.com/paper/2402.15391/) (2024)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [AgiBot World Colosseo: A Large-scale Manipulation Platform for Scalable and Intelligent Embodied Systems](https://mlsanity.com/paper/2503.06669/) (2025)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [MolmoAct: Action Reasoning Models that can Reason in Space](https://mlsanity.com/paper/2508.07917/) (2025)
- [DexCap: Scalable and Portable Mocap Data Collection System for Dexterous Manipulation](https://mlsanity.com/paper/2403.07788/) (2024)
- [Knowledge Insulating Vision-Language-Action Models: Train Fast, Run Fast, Generalize Better](https://mlsanity.com/paper/2505.23705/) (2025)
- [DexGraspNet: A Large-Scale Robotic Dexterous Grasp Dataset for General Objects Based on Simulation](https://mlsanity.com/paper/2210.02697/) (2022)
- [AdaWorld: Learning Adaptable World Models with Latent Actions](https://mlsanity.com/paper/2503.18938/) (2025)
- [Reactive Diffusion Policy: Slow-Fast Visual-Tactile Policy Learning for Contact-Rich Manipulation](https://mlsanity.com/paper/2503.02881/) (2025)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [Riemannian Flow Matching Policy for Robot Motion Learning](https://mlsanity.com/paper/2403.10672/) (2024)
- [Generalizable Humanoid Manipulation with 3D Diffusion Policies](https://mlsanity.com/paper/2410.10803/) (2024)
- [DexGraspNet 2.0: Learning Generative Dexterous Grasping in Large-scale Synthetic Cluttered Scenes](https://mlsanity.com/paper/2410.23004/) (2024)
- [Latent Action Learning Requires Supervision in the Presence of Distractors](https://mlsanity.com/paper/2502.00379/) (2025)
- [CLAM: Continuous Latent Action Models for Robot Learning from Unlabeled Demonstrations](https://mlsanity.com/paper/2505.04999/) (2025)
- [CoMo: Learning Continuous Latent Motion from Internet Videos for Scalable Robot Learning](https://mlsanity.com/paper/2505.17006/) (2025)

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

- [FocalPolicy: Frequency-Optimized Chunking and Locally Anchored Flow Matching for Coherent Visuomotor Policy](https://mlsanity.com/paper/2605.15944/) (2026)
- [EATR-Stereo: Embodiment-Aware Token Routing of Paired Stereo Evidence for Humanoid Vision-Language-Action Control](https://mlsanity.com/paper/2608.17453/) (2026)

## Abstract (arXiv)

Learning long-horizon robotic manipulation requires jointly achieving expressive behavior modeling, real-time inference, and stable execution, which remains challenging for existing generative policies. Diffusion-based approaches offer strong modeling capacity but incur high inference latency, while flow matching enables fast, near-single-step generation yet often suffers from unstable execution when operating directly in the raw action space. We propose Continuous Latent Action Flow Policy (CoLA-Flow Policy), a trajectory-level imitation learning framework that performs flow matching in a continuous latent action space. By encoding action sequences into temporally coherent latent trajectories and learning an explicit latent-space flow, CoLA-Flow Policy decouples global motion structure from low-level control noise, enabling smooth and reliable long-horizon execution. The framework further integrates geometry-aware point cloud conditioning and execution-time multimodal modulation, using visual cues as a representative modality to enhance real-world robustness. Experiments in simulation and on real robots show that CoLA-Flow Policy achieves near-single-step inference, improves trajectory smoothness by up to 93.7% and task success by up to 25 percentage points over raw action-space flow baselines, while remaining significantly faster than diffusion-based policies.