# Dense-Jump Flow Matching with Non-Uniform Time Scheduling for Robotic Policies: Mitigating Multi-Step Inference Degradation

arXiv: https://arxiv.org/abs/2509.13574 · HTML: https://mlsanity.com/paper/2509.13574/

## 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 15 of its 22 references that are in the map.
- First posted on arXiv 16 Sep 2025.

## 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, 15 of 15)

- [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)
- [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)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024)
- [AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies](https://mlsanity.com/paper/2402.04292/) (2024)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Flow Matching Imitation Learning for Multi-Support Manipulation](https://mlsanity.com/paper/2407.12381/) (2024)
- [CIFAR-10: KNN-based Ensemble of Classifiers](https://mlsanity.com/paper/1611.04905/) (2016)
- [Robot Shape and Location Retention in Video Generation Using Diffusion Models](https://mlsanity.com/paper/2407.02873/) (2024)
- [UGOD: Uncertainty-Guided Differentiable Opacity and Soft Dropout for Enhanced Sparse-View 3DGS](https://mlsanity.com/paper/2508.04968/) (2025)

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

- [Velocity Scheduled Flow Matching](https://mlsanity.com/paper/2607.11442/) (2026)
- [x-Prediction Is All You Need:Training-Free Accelerated Generation via Endpoint Decodability](https://mlsanity.com/paper/2607.06114/) (2026)

## Abstract (arXiv)

Flow matching has emerged as a competitive framework for learning high-quality generative policies in robotics; however, we find that generalisation arises and saturates early along the flow trajectory, in accordance with recent findings in the literature. We further observe that increasing the number of Euler integration steps during inference counter-intuitively and universally degrades policy performance. We attribute this to (i) additional, uniformly spaced integration steps oversample the late-time region, thereby constraining actions towards the training trajectories and reducing generalisation; and (ii) the learned velocity field becoming non-Lipschitz as integration time approaches 1, causing instability. To address these issues, we propose a novel policy that utilises non-uniform time scheduling (e.g., U-shaped) during training, which emphasises both early and late temporal stages to regularise policy training, and a dense-jump integration schedule at inference, which uses a single-step integration to replace the multi-step integration beyond a jump point, to avoid unstable areas around 1. Essentially, our policy is an efficient one-step learner that still pushes forward performance through multi-step integration, yielding up to 23.7% performance gains over state-of-the-art baselines across diverse robotic tasks.