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

• The action head accounts for about 40% of desktop-GPU end-to-end inference time and up to 50% on robotic edge platforms, motivating fewer denoising steps.Source: §1 · pp. 1–2
• Unlike image generation’s stable, narrow local acceleration, RFMs surge late and show widening acceleration spread, making direct MeanFlow adaptation unstable.The surge reaches 76× its initial value at t = 1; widening spread is associated with amplified estimation errors.Source: §1 · pp. 2–3
• K-MF uses a kinematic identity to split the time-derivative estimate across two sub-intervals, covering early and late denoising while anchoring the estimate against spread-driven error amplification.Source: §1 · p. 3
• A fixed midpoint outperforms uniform random sampling, while a learnable intermediate point conditioned on t and r performs best among the considered strategies.Source: §1 · p. 3
• K-MF supports one-step action generation with performance comparable to multi-step flow matching across training paradigms, RFMs, datasets, and Sim2Sim and Real2Sim evaluations.Source: §1 · p. 3

• Image-generation approaches reduce sampling steps through distillation or consistency models, while MeanFlow predicts average velocity and some interval-partition methods target training efficiency or stability.Source: §2 · p. 3
• Robotics specialist policies use consistency constraints for imitation learning and behavioral cloning, while recent MeanFlow adaptations target imitation learning and reinforcement learning.Source: §2 · p. 3
• Few- or one-step generation in generalist RFMs remains underexplored; prior work applies image methods directly or evaluates limited tasks and models, unlike K-MF’s broader validation.Source: §2 · p. 3
• K-MF addresses long-interval derivative errors from late-stage surges and widening spread by splitting estimation across two sub-intervals, stabilizing MeanFlow’s bootstrapping process.Source: Figure 2 · p. 4

3.1 PRELIMINARIES

• In the preliminaries, RFMs use a transformer action head to predict action chunks, and MeanFlow's average-velocity prediction permits one-step generation from t = 1 to r = 0.The flow-matching path interpolates between a target action chunk and Gaussian noise; the RFM conditions on visual, language, and proprioceptive inputs.Source: §3.1 · p. 4

3.2 KINEMATIC MEANFLOW

• MeanFlow's derivative bootstrapping breaks down in RFMs: late-stage acceleration increases estimation errors, while widening spread amplifies them and destabilizes training.This makes reliable one-step action generation difficult with direct MeanFlow application.Source: §3.2 · p. 5
• K-MF decouples the MeanFlow time-derivative term across two sub-intervals along the same flow path, addressing RFM-specific velocity-field estimation difficulties.The full-interval average velocity is represented as a convex combination of the two sub-interval average velocities.Source: §3.2 · p. 5
• The K-MF policy is trained by minimizing mean-squared error against a decoupled target, with both sub-interval states constructed along the conditional flow path.For a given action chunk, the two conditional instantaneous velocities are equal to ϵ − a.Source: §3.2 · p. 5
• K-MF considers random, fixed-midpoint, and learnable strategies for setting the intermediate point that determines the sub-interval split.The learnable strategy generates the temporal ratio with a three-layer MLP; the supplied passage also describes early- and late-training considerations for the split.Source: §3.2 · pp. 5–6
• Random and fixed-midpoint K-MF add no hyperparameters over MeanFlow, while the learnable strategy adds α and γ.For the learnable strategy, γ increases linearly from −0.5 to 0.5 during training, and its generator loss updates ϕ while holding policy parameters θ constant.Source: §3.2 · p. 6

4.1 SETUPS

• Evaluation covers four training datasets and Sim2Sim and Real2Sim settings, comparing GR00T-N1.6 fine-tuning and SimVLA-S training from scratch against multi-step flow matching and MeanFlow variants.The datasets are LIBERO, BridgeData V2, Fractal, and a COMPASS-generated PointNav dataset.Source: §4.1 · p. 6

4.2 PILOT EXPERIMENTS

• In pilot tests, K-MF achieves one-step generation with performance comparable to multi-step flow matching, while MVP fails to produce viable actions and α-Flow degrades.MeanFlow requires a delicate training recipe and remains sensitive to the separated timestep.Source: §4.2 · p. 7, Figure 3 · p. 7

4.3 MAIN RESULTS

• On LIBERO, K-MF is competitive with or superior to multi-step flow matching and two-step MeanFlow for fine-tuning GR00T-N1.6 and training SimVLA-S from scratch.These results cover both fine-tuning and training from scratch.Source: §4.3 · p. 7, Table 2 · p. 7
• K-MF achieves higher success rates than multi-step flow matching in most evaluated settings across fine-tuning datasets, evaluation settings, and robotic embodiments.The evaluation includes tabletop manipulation and PointNav, spanning small-scale simulation data and larger real-world datasets.Source: Table 3 · p. 8, §4.3 · p. 8

4.4 ABLATION STUDIES

• The learnable strategy performs best for choosing c, midpoint partitioning is a straightforward fast-adaptation option, and random sampling performs worse.The reported efficacy is attributed primarily to improved time-derivative estimation rather than augmentation from different partitions.Source: §4.4 · p. 8, Table 4 · p. 8
• K-MF reduces action-head latency by 67.5%–74.4% and end-to-end latency by 30.3%–54.9% across hardware platforms and execution modes.Training time rises by 7.5%–13.6% and peak GPU memory by at most 2.5% versus MeanFlow.Source: §4.4 · p. 8, Table 5 · p. 9

4.5 UNDERSTANDING THE DYNAMICS IN THE VELOCITY FIELD OF RFMS

• Across RFMs, local acceleration magnitudes rise during denoising, while their spread varies with the dataset and increases with task diversity.For Fractal, the relative spread follows an approximately logarithmic trend at low task counts and a saturating power-law trend at higher counts.Source: Figure 5 · p. 9, §4.5 · p. 9

5 CONCLUSION

• K-MF decomposes the overall time derivative into two sub-interval terms and incorporates three strategies for choosing intermediate points.The framework targets one-step action generation in generalist RFMs.Source: §5 · p. 9
• K-MF generally achieves superior performance to multi-step flow matching across diverse settings.Source: §5 · p. 9
• K-MF adds training overhead compared with flow matching, but its overall training cost remains reasonable.Evaluation does not cover whole-body control or dexterous manipulation, which remain challenging for current RFMs.Source: §5 · p. 9

AI USE STATEMENT

• AI tools were used solely to assist with proofreading, and the authors manually reviewed all AI-assisted edits.Source: AI USE STATEMENT · p. 10

APPENDIX

• The appendix covers training datasets, baseline implementation details, experimental setups, and further K-MF ablations.Source: APPENDIX · p. 13
• Appendix Section E discusses two important problems.Source: APPENDIX · p. 13

A DATASETS

• LIBERO comprises four simulation task suites covering spatial relationships, object variations, goal variations, and long-horizon execution, with 2K trajectories across 40 tasks.Each suite contains 10 tasks with 50 trajectories per task.Source: A DATASETS · p. 13
• Fractal contains 87K real-world manipulation trajectories across 599 tasks, mainly covering varied kitchen manipulation behaviors.Source: A DATASETS · p. 13
• BridgeData V2 contains 53K real-world manipulation trajectories spanning 13 skills across 24 environments.The data includes variation in objects, camera viewpoints, and workspace configurations.Source: A DATASETS · p. 13
• The COMPASS-generated PointNav dataset contains 658 synthetic Unitree G1 navigation trajectories with robot state, egocentric RGB observations, and velocity-command actions.Source: A DATASETS · p. 13

B.1 FLOW MATCHING

• Flow matching is the selected RFMs' original method, reproduced mainly with official settings and minor hyperparameter adjustments.Source: §B.1 · p. 13

B.2 MEANFLOW

• MeanFlow uses progressive schedules that increase the flow ratio from 0 to 0.5 and the gap scale from 0 to 1.The flow-ratio schedule reduces samples with t = r from 100% to 50%, while the gap-scale schedule expands sampled temporal gaps from zero to their original magnitudes.Source: §B.2 · p. 13
• Progressive timestep sampling shifts MeanFlow training from local average-velocity learning early on to the standard objective.Source: §B.2 · p. 13

Other MeanFlow Variants

• Progressive sampling gradually shifts MeanFlow training from traditional flow matching to its standard formulation, but K-MF does not require this strategy.The flow ratio controls the proportion of t ≠ r samples, while the gap scale bounds the interval t − r.Source: §B.3 · p. 14

Hyperparameter Settings

• The experiments specify separate flow-matching and K-MF hyperparameters across SimVLA-S and GR00T-N1.6 settings.The listed settings include batch size, learning rate, optimizer, training steps, timestep sampling, and image resolution.Source: §B.3 · p. 14

Other MeanFlow Variants

• α-Flow transitions from instantaneous to average velocity learning over 12,000 iterations, with a 4,000-iteration interval-partitioning phase between them.The model learns instantaneous velocity for the first 8,000 iterations and average velocity after 12,000 iterations.Source: §B.3 · p. 14
• MVP stabilizes action-generation training by augmenting the MeanFlow objective with an equally weighted auxiliary instantaneous-velocity loss.It otherwise retains the flow-matching baseline training recipe.Source: §B.3 · p. 14

Implementation

• Training experiments run on one node with 8×H20 GPUs, and K-MF and baselines use the official GR00T-N1.6 and SimVLA codebases.The experiments mainly follow the standard training recipe, with hyperparameters summarized in Table A.Source: C EXPERIMENTAL SETUPS · p. 15

Evaluation Setups

• Experiments evaluate on LIBERO, SimplerEnv, and COMPASS using each codebase’s standard protocol.COMPASS covers in-distribution and out-of-distribution navigation settings, with the hospital scenario representing OOD.Source: C EXPERIMENTAL SETUPS · p. 15
• LIBERO evaluation covers four 10-task suites, with 200 rollouts per suite on GR00T-N1.6 and 500 on SimVLA-S.The suites are Spatial, Object, Goal, and Long, totaling 40 tasks.Source: C EXPERIMENTAL SETUPS · p. 15
• SimplerEnv evaluates Fractal- and BridgeData V2-trained models on GoogleX and WidowX manipulation tasks, using 200 rollouts per task.GoogleX tasks span manipulation skills; WidowX tasks vary target objects.Source: C EXPERIMENTAL SETUPS · p. 15

Hyperparameters α and γ

• α = 0.1 achieves the best result, while constraining γ to a moderate range such as [−0.5, 0.5] yields better performance.α balances the generator loss relative to the whole network; γ controls the penalty for discrepancies between overall and decoupled estimates.Source: D MORE ABLATION STUDIES · p. 15

Flow Ratio

• K-MF maintains strong performance at a flow ratio of 0.75 and is relatively insensitive to the flow ratio within the tested range.The flow ratio is the fraction of samples with t ≠ r in each training batch.Source: D MORE ABLATION STUDIES · p. 15

Learnable Generator Gϕ

• The three-layer Gϕ achieves a 97.9% success rate, versus 97.3% for two layers, while a fourth layer adds no further improvement.The adopted three-layer MLP has dimensions 2 → 128 → 128 → 1 and maps its output into (0, 1).Source: D MORE ABLATION STUDIES · p. 15
• The mean generated λ eventually converges to approximately 0.48, and trained λ distributions show a consistent overall trend across datasets.The distributions are more concentrated on larger datasets, where the learnable generator also yields greater gains than on smaller datasets.Source: D MORE ABLATION STUDIES · p. 16

Error Amplification

• A 1% early-timestep perturbation produces an error in dut,r/dt approximately 120× its initial magnitude by the end of denoising.Amplification decreases when perturbations are introduced at later timesteps (t < 0.6); the authors attribute mitigation in K-MF to independent, additive error accumulation across its two terms.Source: D MORE ABLATION STUDIES · p. 16

Error Amplification

• In SimVLA-S, Figure D measures relative amplification of dut,r/dt after a 1% perturbation to zt across denoising timesteps.The curve reports the mean over 50 random trials.Source: Figure D · p. 17, E DISCUSSION · p. 17

RFM and Image-Generation Dynamics

• Across LIBERO and ImageNet, Figure E compares local acceleration, speed-change rate, and angular-change rate over denoising.The figure presents SimVLA-S and DiT-B results and visualizes spread using the 1.5-IQR interval across 4K samples.Source: E DISCUSSION · p. 17

Why K-MF Samples zc Along the Conditional Flow Path

• Constructing zc along the conditional flow path avoids basing the second derivative evaluation on the model’s estimated intermediate state.This avoids inheriting prediction errors in zc from the first estimation and lets the two derivative evaluations run in parallel.Source: E DISCUSSION · p. 17

Why One-Step Generation Is Challenging

• RFMs’ late-stage changes in speed and angular direction contribute jointly to the local-acceleration surge, while early velocity changes allow longer flow-matching intervals.For one-step generation, local-global inconsistency complicates estimating the time derivative, and widening acceleration spread amplifies estimation errors.Source: E DISCUSSION · p. 18

Discussion

• As RFMs scale to larger datasets and more complex, high-DoF embodiments, the identified one-step generation difficulties may become more pronounced.Source: E DISCUSSION · p. 18