Kinematic MeanFlow: One-Step Action Generation Policy for Robotic Foundation Models

Jiawei Fan; Sifeng Wang; Yuqing Hou; Anbang Yao

cs.ROOct 1, 2026

Kinematic MeanFlow: One-Step Action Generation Policy for Robotic Foundation Models

Authors: Jiawei Fan, Sifeng Wang, Yuqing Hou, Anbang Yao

Organizations: Intel Labs China · Midea AI Research

Abstract

In this paper, we study how to achieve one-step action generation in Robotic Foundation Models (RFMs), aiming to overcome the high inference latency of multi-step flow matching. MeanFlow provides a promising framework for this goal, yet its direct application leads to performance collapse. We discover that this stems from two distinctive dynamics exhibited in the RFM velocity field: (1) the ``local acceleration" exhibits stability early on, but surges sharply towards the end of the denoising process, and (2) the spread of its magnitudes across samples widens as denoising progresses. To address these issues, we introduce Kinematic MeanFlow (K-MF), a novel one-step action policy tailored for RFMs. Specifically, grounded in a kinematic identity, K-MF decouples the time derivative term in the MeanFlow formulation into two sub-interval terms separated by an intermediate point. This decoupled formulation enables the two terms to capture early-stage and late-stage denoising dynamics, respectively, while mitigating the error amplification across the process. As a result, our K-MF empowers RFMs to achieve one-step action generation in both training from scratch and fine-tuning paradigms across diverse tasks, while outperforming multi-step flow matching in most settings. In terms of inference efficiency, K-MF reduces action-head latency of GR00T-N1.6 by 67.5%~74.4% across L40 and Jetson Orin in eager and compiled modes, yielding end-to-end latency reductions of 30.3%~54.9%. Code will be available at https://github.com/IntelChina-AI/K-MF.

Figures & tables

Panel of Figure 1 — Figure 1: Illustrations of our key observations. In (a), we calculate the change in average velocity $\Delta\mathbf{u}$ over a time interval of $\Delta t=0.05$ and compare the dynamics of image generation (DiT-B on ImageNet) and action generation (SimVLA-S paired with DiT-B on LIBERO). To highlight the trend, we use the relative value to the initial value of each domain. The shaded area is bounded by the standard 1.5-IQR fences. In (b), we compare the loss landscapes of standard MeanFlow and our proposed K-MF, both applied to SimVLA-S on LIBERO. More examples are shown in Figure 5 .

Figure 2: Comparison of MeanFlow and our Kinematic MeanFlow (K-MF). In RFM velocity fields, the late-stage surge and widening spread shown in (a) lead to large errors in estimating the time derivative of average velocity over long intervals. These errors cause MeanFlow’s bootstrapping loop to collapse. In contrast, K-MF splits time-derivative estimation across two sub-intervals, mitigating these errors and stabilizing the bootstrapping process. Note that the ideal target is a conceptual reference for better illustration. More detailed analysis is in Section 3.2 .

Table 1: Pilot studies on MeanFlow and its variants on GR00T-N1.6. In (a), we study the delicate training recipe for MeanFlow, including gradient clipping, progressive sampling for timesteps, and sufficient training iterations. In (b), we compare the performance between selected baselines and our K-MF (learnable strategy). NFE denotes the number of function evaluations, SR is the success rate on the LIBERO-10 benchmark, and * denotes the delicate recipe. Best results are bolded .

Model	# Params	Training Paradigm	Method	# Iters	NFE	Spatial	Object	Goal	Long	Avg.
\Block 3-1GR00T-N1.6	\Block 3-13B	\Block 3-1Fine-tuning	Flow Matching	20K	4	97.5	98.5	98.5	94.5	97.3
			MeanFlow*	60K	2	96.5	99.0	95.5	87.0	94.5
			Ours	20K	1	99.5	99.5	98.0	94.5	97.9
\Block 3-1SimVLA-S	\Block 3-10.6B	\Block 3-1Training from scratch	Flow Matching	200K	10	97.0	97.4	98.0	84.2	94.2
			MeanFlow*	200K	2	95.8	97.2	97.8	84.0	93.7
			Ours	200K	1	96.4	97.8	98.4	87.8	95.1

Table 2: Performance comparison across two training paradigms on the LIBERO benchmark. We compare flow matching, MeanFlow (NFE=2), and our K-MF (learnable strategy, NFE=1) under both fine-tuning on GR00T-N1.6 and training from scratch on SimVLA-S (without pre-training on action data). * denotes the delicate recipe in Table 1(a) . Best results are bolded .

Figure 3: Sensitivity to the separated timestep of two-step generation, under the best setting in Table 1(a) .

\Block 2-1 Task Type	\Block 2-1 Dataset	\Block 2-1 Setting	\Block 2-1 Embodiment	\Block 2-1 Task	FM	Ours
					(NFE = 4)	(NFE = 1)
\Block 10-1Tabletop
Manipulation	\Block 5-1Fractal	\Block 5-1Real2Sim	\Block 5-1GoogleX	Pick	91.0	91.0
				Move	87.5	92.0
				Open	35.5	50.5
				Close	81.5	80.0

Table 3: Performance comparison across benchmarks and embodiments. We compare multi-step flow matching (FM) with our one-step K-MF across different fine-tuning datasets, evaluation settings, and robotic embodiments. Best results are bolded .

Table 5: Efficiency analysis of K-MF. In (a), we show the inference latency (ms) of flow matching and K-MF on GR00T-N1.6. AH and E2E denote action head and end-to-end latency, respectively. In (b), we show training overhead, in terms of peak GPU memory (GB) and training time (hours), under the same settings as in Table 2 , except keeping the same training iterations for fair comparison.

Panel of Figure 5 — Figure 5: More illustrations of the RFM velocity field. (a) Comparison of dynamics between SimVLA-S and GR00T-N1.6 on LIBERO. (b) Dynamics of GR00T-N1.6 on LIBERO vs. Fractal. (c) Relative spread of local acceleration magnitudes as the number of tasks increases.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A: Illustration of progressive sampling. This strategy is governed by the flow ratio (which determines the proportion of $t\neq r$ ) and the gap scale (which defines the maximum interval for $t-r$ ). Initially, the training process reduces to traditional flow matching. As training progresses, the sampling of $t$ and $r$ gradually transitions to the standard formulation. Note that this strategy is exclusively applied to MeanFlow; our proposed K-MF does not require this technique.

Category	Hyperparameter	SimVLA-S	GR00T-N1.6
Category	Hyperparameter	LIBERO	LIBERO	Fractal/Bridge	PointNav
Shared	Global batch size	256	640	1024	64
	Learning rate	1.00e-04	1.00e-04	1.50e-04	1.00e-04
	Optimizer	AdamW	AdamW	AdamW	AdamW
	Betas	(0.9, 0.95)	(0.9, 0.95)	(0.9, 0.95)	(0.9, 0.95)
	Weight decay	0.0	1.00e-05	1.00e-05	1.00e-05

Appendix

Table A: Hyperparameter settings of the flow matching baseline and our K-MF.

Table B: Ablation studies on the LIBERO benchmark. We evaluate the hyperparameters

\alpha

and

\gamma

in the learnable strategy, the flow ratio inherited from MeanFlow (determining the proportion of

t\neq r

per batch), and the depth of

G_{\phi}

Panel of Figure 14 — Figure C: Ablation studies on learnable generator $G_{\phi}$ on GR00T-N1.6. In (a), we illustrate the variation trend of the mean generated $\lambda$ throughout the training on LIBERO. In (b), we study the distribution of $\lambda$ generated by the well-trained $G_{\phi}$ on LIBERO and Fractal datasets. As the four task suites in LIBERO share very similar properties, we use LIBERO-10 as the representative case.

Figure D: Relative error amplification across denoising timesteps. On SimVLA-S, we introduce a 1% random perturbation on $\mathbf{z}_{t}$ , where $t\in\{1,0.9,\ldots,0.1\}$ , and measure the relative amplification to the initial perturbation in $\frac{d\mathbf{u}_{t,r}}{dt}$ at $r\leq t$ . The curve shows the mean value over 50 random trials.

Panel of Figure 16 — Figure E: The absolute rate of velocity change (local acceleration), rate of speed change, and rate of angular change for models trained on LIBERO and ImageNet (top: SimVLA-S; bottom: DiT-B) . Throughout the denoising process, we compute the average velocity over uniform timesteps, maintaining a constant interval $\Delta t=0.05$ . We visualize the spread of magnitudes using the interval $[Q_{1}-1.5\mathrm{IQR},Q_{3}+1.5\mathrm{IQR}]$ , defined by the standard 1.5-IQR rule for identifying potential outliers. Here, $\mathrm{IQR}=Q_{3}-Q_{1}$ is the interquartile range, with $Q_{1}$ and $Q_{3}$ denoting the 25th and 75th percentiles, respectively. Values outside this interval are considered potential outliers and excluded from visualization. Each curve is aggregated over 4K samples (action chunks for LIBERO and images for ImageNet), consistent with the setup in Figure 1(a) and Figure 5 of the main paper.

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Faster Visuomotor Policy Learning on Action Manifolds via Riemannian MeanFlow

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Open paper AskPDF arXiv

Visuomotor policies learn a direct map from raw sensory observations to robot action sequences. Policies based on Diffusion and Flow Matching capture the multimodal distribution over action sequences in an end-to-end manner. This expressivity comes at the cost of multi-step numerical integration of the learned vector field for action generation, which can be expensive and time-consuming, impeding fast control rates required in robotics applications. Furthermore, robot action sequences are usually defined on a smooth, differentiable manifold, requiring that the learned policy respects the intrinsic geometry of the robot's action space. Here, we present Riemannian MeanFlow Policy (RMFP), which learns the conditioned flow map of the probability path on the robot action manifold. Our formulation employs a flow map consistency objective grounded in the data by a Riemannian Conditional Flow Matching anchor. The flow map consistency condition is stable to train and constrains the learned model to finite-time transport, which yields on-manifold action sequence generation with as few as one network function evaluation. We present results on the spherical LASA and Push-T benchmarks, on the Tool Hang and Transport tasks of the Robomimic suite, and on the Franka Kitchen task with manifold-constrained action generation, and demonstrate that RMFP attains performance competitive with prior work at a lower sampling cost. We also employ RMFP on a real-world robotic manipulation task to demonstrate fast action generation under imperfect sensor measurements in the physical world.

Abstract

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