# Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generation

arXiv: https://arxiv.org/abs/2606.20135 · HTML: https://mlsanity.com/paper/2606.20135/

## 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 43 of its 49 references that are in the map.
- First posted on arXiv 18 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 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (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)
- [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)
- [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)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [Open X-Embodiment: Robotic Learning Datasets and RT-X Models](https://mlsanity.com/paper/2310.08864/) (2023)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics](https://mlsanity.com/paper/2506.01844/) (2025)
- [CogACT: A Foundational Vision-Language-Action Model for Synergizing Cognition and Action in Robotic Manipulation](https://mlsanity.com/paper/2411.19650/) (2024)
- [X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Model](https://mlsanity.com/paper/2510.10274/) (2025)
- [π*0.6: a VLA That Learns From Experience](https://mlsanity.com/paper/2511.14759/) (2025)
- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [π0.7: a Steerable Generalist Robotic Foundation Model with Emergent Capabilities](https://mlsanity.com/paper/2604.15483/) (2026)
- [Flow as the Cross-Domain Manipulation Interface](https://mlsanity.com/paper/2407.15208/) (2024)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [GR-3 Technical Report](https://mlsanity.com/paper/2507.15493/) (2025)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [DexGraspVLA: A Vision-Language-Action Framework Towards General Dexterous Grasping](https://mlsanity.com/paper/2502.20900/) (2025)
- [Equivariant Diffusion Policy](https://mlsanity.com/paper/2407.01812/) (2024)

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

- [Frequency-Conditioned Flow Matching for Vision-Language-Action Models](https://mlsanity.com/paper/2609.10405/) (2026)

## Abstract (arXiv)

Flow matching has emerged as a standard paradigm for robotic manipulation owing to its strong expressive power for modelling complex, multimodal action distributions, alongside similar approaches like diffusion policy. However, existing methods rely on discretized action chunks, making them brittle to demonstrations collected at heterogeneous control frequencies and prone to temporally inconsistent actions that degrade control stability. In this paper, we propose Frequency-Aware Flow Matching (FAFM), which outputs continuous, temporally consistent actions. To handle heterogeneous frequency input, we transform discrete action sequences into the frequency domain with the discrete cosine transform (DCT), perform flow matching over the resulting coefficients, and reconstruct continuous actions via cosine basis expansion. To generate temporally consistent actions, we regularize the first-order temporal derivative to promote smooth actions. This corresponds to a Sobolev-type constraint that suppresses high-frequency errors and discourages abrupt action changes. Our FAFM is simple, introduces no additional network parameters and applies to standalone flow-matching policies and vision-language action models. Across synthetic toy benchmark, obstacle avoidance, LapGym, and LIBERO, FAFM improves success rates, multimodal expressivity, motion smoothness, convergence speed, robustness to mechanical bias and mixed-frequency input. These gains are consistent when deployed on a real-world Franka robot. Code available at https://anonymous.4open.science/r/FAFM.