Source-linked AI summary
Adaptive Mean Flow for Responsive Closed-Loop Robot Control
Aksel Vaaler, Marco Job, Christian Holden, Olav Egeland
TL;DR
Existing fast diffusion and flow policies still commonly use action chunks, limiting fully closed-loop responsiveness. AMF combines Mean Flow with variable per-step noise and reuse of the previous action trajectory; it reports stronger performance across simulated and real tasks, with a stated 6% relative improvement over the best-performing simulation baseline.
Problem
Fast diffusion and flow inference methods still commonly use action chunks, and relatively few works directly address the consistency-reactivity trade-off in fully closed-loop, single-step execution.
Source: B. Consistency-reactivity trade-off in… · p. 2Method
AMF uses per-step flow intervals and a sequence initialized around the previous action trajectory to make rapid closed-loop predictions while balancing consistency and flexibility.
Source: B. Consistency-reactivity trade-off in… · p. 2, §III · pp. 3–4Results
AMF achieves a 6% relative improvement over the best-performing baseline, AFM, in the main simulation results and performs best overall on real Push-T and Box-close, significantly outperforming baselines on real Push-T.
Source: C. Results · p. 5, A. Results · p. 7Takeaways & Limitations
AMF demonstrated efficacy on simulated and real-world tasks with and without dynamic components, supporting its use for responsive, smooth robot control within those evaluated settings.
Source: §VI · pp. 7–8AMF treats all action modalities alike despite being designed primarily for continuous modalities, and commonly failed to open or close the gripper when required.
Source: §VI · p. 8
Abstract
from arXiv · showhide
Diffusion- and flow-based robot policies have recently become widespread in robotic Imitation Learning (IL) due to their high performance and ability to model continuous and multimodal distributions. However, the iterative denoising procedure used by these models introduces significant prediction latency, hindering high-frequency closed-loop robot control and leading to jittery, unstable motion when frequent updates to the robot's action predictions are used. Therefore, it is common practice to train models to predict chunks of actions that can be executed sequentially without feedback, even when this reduces responsiveness and may mean the most recent state information is not used. In this article, we present Adaptive Mean Flow (AMF), a flow-based IL method that enables smooth and responsive, fully closed-loop robot control. AMF uses Mean Flow, which is an accelerated form of Flow Matching (FM), to minimize prediction latency. To ensure smoothness and consistency across predictions, AMF uses a corrupted version of the trajectory from the previous step when predicting new robot actions, with the signal-to-noise ratio increasing over the time parameter of the trajectory. This discourages large changes in the prediction from one step to the next, while allowing freedom to adapt the predictions for future steps. We evaluate AMF across a wide range of simulated and real robot tasks and demonstrate significantly improved performance compared with baselines. Code: https://github.com/akselva/Adaptive-mean-flow-RoboticIL.
I. RELATED WORK
Prior work accelerates diffusion and flow inference to reduce prediction latency, but AMF uses Mean Flow for single-step action prediction without distillation, extra consistency losses, or complex inference algorithms.
I. RELATED WORK
- Diffusion and flow policies need multiple denoising or integration steps, motivating samplers and consistency methods that reduce inference computation,,,,.Streaming approaches also vary noise across the action sequence or treat a flow step as a forward robot-trajectory step,,.Source: A. Speeding up diffusion and flow… · p. 2
- Streaming Flow Policy treats a flow-ODE step as a forward robot-trajectory step, making the next action available after one integration step.Other streaming methods use varying noise levels so near-future actions need fewer denoising steps,.Source: A. Speeding up diffusion and flow… · p. 2
- AMF uses Mean Flow to predict action sequences in one step without distillation, extra consistency losses, or complex inference algorithms [8],.Mean Flow had also been used in.Source: A. Speeding up diffusion and flow… · p. 2
B. Consistency-reactivity trade-off in robotic Imitation Learning
Faster diffusion and flow inference can smooth policy execution, but existing approaches still commonly rely on action chunks. AMF instead uses dynamic per-step noise and previous predictions to balance consistency with responsiveness in closed-loop control.
B. Consistency-reactivity trade-off in robotic Imitation Learning
- Faster inference can smooth policy execution, but the cited approaches still use action chunking and therefore do not fully use the responsiveness of fast inference.Few works directly address the consistency-reactivity trade-off between chunked and fully closed-loop single-step execution.Source: B. Consistency-reactivity trade-off in… · p. 2
- Bidirectional Decoding and Past-Token Prediction select among candidate sequences, while Self-Guided Action Diffusion [20] and Real-Time Chunking steer predictions toward previous trajectories.Temporal Action Selection [22] uses online RL fine-tuning to adapt an action selector.Source: B. Consistency-reactivity trade-off in… · p. 2
- AMF avoids fine-tuning and additional test-time compute by training with dynamic per-step signal-to-noise ratios and initializing each rapid closed-loop prediction around the previous trajectory.This retains flexibility in policy behavior while maintaining consistency through the previous prediction.Source: B. Consistency-reactivity trade-off in… · p. 2
II. BACKGROUND
Flow Matching learns a velocity field that transports samples from a prior toward the data distribution, while Mean Flow models average velocity over an interval to enable direct sampling. The paper adapts these approaches to conditional robot action-sequence prediction.
II. BACKGROUND
- Flow Matching learns a velocity field transporting samples from a known prior, typically Gaussian, toward approximate samples from the unknown data distribution,.For a linear schedule, the interpolated sample is z_s = s x + (1 − s)e and its conditional velocity is x − e.Source: §II · p. 2
- The Flow Matching objective regresses a neural network toward conditional velocity, and samples are generated by integrating its learned velocity field from prior noise.The paper states that this objective approximates the marginal velocity.Source: §II · p. 2
- Mean Flow models average velocity over an interval because the marginal velocity field can be curved and require several ODE integration steps for high-quality samples.The mean-flow identity supplies a tractable training objective, with a derivative-based target and stop-gradient loss.Source: §II · p. 3
- For robotic imitation learning, the policy conditions on recent observations and predicts action sequences drawn from the expert’s conditional action distribution.The action horizon includes future steps and the current action; the observation horizon specifies past observations, and the Mean Flow policy uses its learned network to generate action sequences.Source: §II · p. 3
III. ADAPTIVE MEAN FLOW
AMF predicts action sequences from a shifted version of the previous trajectory rather than starting from pure noise. Per-step flow intervals vary the corruption across the sequence, retaining consistency for overlapping actions while allowing future actions to adapt.
III. ADAPTIVE MEAN FLOW
- AMF uses Mean Flow’s direct action sampling for tighter closed-loop control, addressing jitter that can arise when frequent replanning lets the policy switch behavior modes.The previous sequence anchors the new prediction where their predicted actions correspond to the same timesteps.Source: §III · p. 3
- The prior sequence is shifted forward by removing its first action and copying its last, then reused as the anchor for the new prediction.The resulting sequence represents the overlap with the previous prediction conditioned on the previous observation.Source: §III · p. 3
- Increasing the uniform noise index gives the previous prediction more influence, but AMF instead varies noise across the sequence so past and current actions stay closer while future actions can change.This targets the desired consistency-reactivity balance for the overlapping and future portions of the trajectory.Source: §III · p. 3
- At inference, AMF uses per-step interval vectors S and R, keeping S constant for past actions and decreasing it monotonically across the current and future action steps.The final index is s_b, with s_b < s_a; γ determines the approach rate, and experiments set s_b = 0.0, s_a = 0.5, and γ = 1.5.Source: §III · p. 3
- Training mixes independently sampled per-step intervals with samples following the monotonic inference schedule; the independent regime increases interval diversity while the scheduled regime better matches inference.For the scheduled regime, S follows the adaptive schedule and R is sampled as a constant across the sequence.Source: §III · p. 4, Figure 3 · p. 4
- AMF conditions each action token on its flow intervals using concatenation, addition, or feature-wise Adaptive LayerNorm-Zero, which parameterizes zero-initialized normalization layers.The paper also predicts past actions and aligns them with the true past trajectory, a strategy associated with improved temporal consistency and overall performance.Source: §III · p. 4
IV. SIMULATION EXPERIMENTS
The section presents simulated experiments to assess AMF’s overall efficacy and investigate key design choices.
IV. SIMULATION EXPERIMENTS
- The experiments are simulated.They are presented to evaluate the proposed method’s overall efficacy and investigate design choices.Source: §IV · p. 5
- The study evaluates the overall efficacy of AMF.Source: §IV · p. 5
- The study investigates key algorithmic and architectural design choices.Source: §IV · p. 5
A. Simulation environments
The simulated evaluation spans Metaworld, Push-T, Dynamic Block Push, and D3IL tasks, with varied manipulation demands and demonstration datasets.
A. Simulation environments
- Eight challenging Metaworld object-manipulation tasks assess varied, precise, and smooth robot manipulation.The tasks use 100 expert demonstrations each and 3DOF end-effector velocities with gripper open/close actions.Source: A. Simulation environments · p. 5
- Push-T tests alignment of a T-shaped object using 90 multimodal human-teleoperation demonstrations.Smoothness and temporal mode consistency matter for solving the task.Source: A. Simulation environments · p. 5
- Dynamic Block Push requires pushing red and green blocks into either of two randomly drifting goal zones.Its dataset contains 1,000 episodes.Source: A. Simulation environments · p. 5
- D3IL Stack-1 and Stack-2 test stacking one or two blocks using diverse human-collected demonstrations.The tasks contain multiple solution strategies; the dataset size is 1,000 episodes.Source: A. Simulation environments · p. 5
- Correlated action noise is added in additional experiments to test responsiveness and robustness to end-effector perturbations.Source: A. Simulation environments · p. 5
B. Baselines
The baselines vary flow method, action execution horizon, and inference strategy, while sharing a transformer policy architecture.
B. Baselines
- FM-8, FM-1, and FM-RTC use Flow Matching with 10 denoising iterations; their action execution differs by chunking or real-time chunking.FM-8 replans every eight steps, FM-1 executes single steps, and FM-RTC uses past predictions for consistency.Source: B. Baselines · p. 5
- Other comparisons include AFM, SDP, and Consistency Policy; SDP and CP are evaluated with single-step execution.AFM uses Flow Matching in place of Mean Flow; SDP uses variable-noise diffusion, and CP distills a diffusion policy into a single-step student.Source: B. Baselines · p. 5
- MF-8 and MF-1 use single-step Mean Flow prediction, while MF-WS reuses past trajectories with constant noise.MF-WS is evaluated with action chunk length 1 and corruption level s = 0.5.Source: B. Baselines · p. 5
C. Results
AMF performs strongly across the simulation tasks, with reported gains in benchmark performance, trajectory smoothness, and robustness to perturbations.
C. Results
- 6% relative improvement over the best-performing baseline, AFM, is reported for AMF across the simulation tasks.The main results table summarizes the benchmark evaluation.Source: C. Results · p. 5, Table I · p. 6
- AMF exhibits considerably less jerkiness than MF-1, FM-1, and the constant-noise trajectory reuse baseline MF-WS.Smoothness is estimated using the third finite difference of consecutive Cartesian actions; lower values indicate smoother trajectories.Source: C. Results · p. 6, Table II · p. 6
- On Dyn-BP, chunking policies FM-8 and MF-8 perform significantly worse than their single-step variants as blocks must track moving goal zones.Source: C. Results · p. 6
- Feature-wise AdaLN-Zero conditioning for flow intervals and training with both independently sampled and monotonically increasing intervals yield the best ablation performance.Removing end-point conditioning performs almost as well as the base AMF.Source: C. Results · p. 6
- Across two Metaworld tasks, AMF’s success rate consistently degrades the least as end-effector perturbation magnitude increases.Without perturbation, each policy achieves close to 100% success.Source: Figure 4 · p. 6, C. Results · p. 6
- Push-T performance remains relatively stable across the tested noise-corruption levels for AMF and MF-WS.Source: C. Results · p. 6
V. REAL-WORLD EVALUATION
The real-world evaluation spans three manipulation tasks with randomized conditions and varied task demands. It also examines how Push-T scores vary with noise corruption.
V. REAL-WORLD EVALUATION
- Real-world tests cover randomized Push-T and Box-close setups plus conveyor-belt interception under varying belt speeds.Push-T uses a rod to push a T-block, while Box-close requires precise lid placement.Source: §V · pp. 6–7
- Table III reports performance impacts of design variations, distinguishing flow-interval conditioning and monotone-schedule sampling probability p_m.Source: Table III · p. 7
- Figure 5 plots Push-T task score against AMF starting noise s_a and MF-WS constant noise corruption.Source: Figure 5 · p. 7
- Push-T demonstrations use different solution strategies, while the conveyor task requires real-time adaptation to belt speed.Source: §V · p. 7
A. Results
AMF performs best overall in the real-world results and significantly outperforms baselines on real Push-T. The results also describe smoother motion and task-specific failure patterns.
A. Results
- AMF performs best overall and significantly outperforms baselines on real Push-T.Table IV reports static-task results after 600 training epochs over 20 random initial configurations per task.Source: A. Results · p. 7, Table IV · p. 7
- FM-8 and real-time-chunking FM were less smooth than AMF, with abrupt movements causing Push-T misalignment or incorrect Box-close grips.Source: A. Results · p. 7
- On the conveyor task, AMF performs best overall and makes the most consistent fine adjustments to align with the moving block.Source: A. Results · p. 7
- AMF sometimes stalls before task completion; nearly all its Box-close failures involved not releasing the lid after alignment.Source: A. Results · p. 7
VI. CONCLUSION
On the conveyor task, AMF makes adjustments that allow it to catch and grasp the moving block after initially trailing. The conclusion presents AMF as a responsive, smooth robot-control method while noting a limitation for discrete gripper actions.
VI. CONCLUSION
- AMF is presented as a flexible, responsive, smooth robot-control method evaluated on simulated and real-world tasks with and without dynamic components.Source: §VI · pp. 7–8
- Conveyor-belt success-rate experiments cover four belt speeds, with 10 trials per method at each setting.Source: Table V · p. 7
- At a maximum belt speed of 15.3 cm/s, AMF catches and grasps the block after initially trailing; FM-8 and real-time-chunking FM fail in different ways.Source: Figure 7 · p. 8
- The approach treats action modalities alike despite being designed mainly for continuous actions, and gripper open/close failures are common.The authors identify modality-specific strategies as a direction for future work.Source: §VI · p. 8