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Frequency-Guided Action Diffusion via Sub-Frequency Manifold Traversal

Junlin Wang

arXiv:2605.27919v1cs.ROcs.LG

TL;DR

Behavior-cloned diffusion policies can overfit high-frequency noise in human demonstrations, motivating a method that guides generation through progressively expanding sub-frequency manifolds. FGO trains multi-band frequency-conditioned mappings and uses progressive reverse-denoising guidance, achieving strong performance with smoother and more temporally consistent actions across robotic manipulation tasks.

  • Problem

    Full-frequency behavior cloning can overfit high-frequency noise and corrective micro-adjustments in human demonstrations, producing erratic motor commands.

  • Method

    FGO trains mappings to sub-frequency manifolds and progressively guides noisy samples through expanding spectral bands toward the full-frequency data manifold.

  • Results

    FGO consistently outperforms or matches baselines across robotic manipulation benchmarks while improving action smoothness and temporal consistency.

  • Takeaways & Limitations

    FGO suppresses high-frequency noise during denoising while preserving a progression toward full-frequency action trajectories.

  • Takeaways & Limitations

    FGO adds inference-time computational overhead and can occasionally over-smooth trajectories needed for fine-grained manipulation.

Abstract

from arXiv · show

Learning visuomotor policies via behavior cloning typically involves mimicking expert demonstrations collected by human operators. However, natural human demonstrations inherently contain high-frequency noise, such as intermittent jerks, pauses, and action jitter. Training policies to directly imitate these raw trajectories inevitably causes the model to inherit these suboptimal behaviors. This pathology is particularly pronounced in diffusion-based policies, where iterative denoising steps can inadvertently amplify high-frequency artifacts at the expense of meaningful fine-grained details. To address these limitations, we present a novel frequency-based algorithm that enables implicit spectral maneuvering and smooth action generation. Our method, Frequency Guidance Operator (FGO), steers the generation process of diffusion polices by progressively driving the noisy samples through intermediate sub-frequency manifolds with expanding spectral bands. Validated on 15 robotic manipulation tasks from 5 benchmarks, FGO achieves superior performance in enhancing action smoothness and temporal consistency while preserving the details necessary for successful task execution. Project website: https://henrywjl.github.io/frequency-guidance-operator/

1 Introduction

Diffusion policies can overfit high-frequency noise in human demonstrations while attempting to learn difficult full-frequency mappings. FGO addresses this by guiding denoising through expanding sub-frequency manifolds and reports smoother, more temporally consistent actions with improved policy performance.

  • Full-frequency mapping is challenging because low-frequency intents and high-frequency details are temporally entangled in complex nonlinear tasks.
  • Human demonstrations contain high-frequency noise and corrective micro-adjustments, making full-spectrum behavior cloning vulnerable to spurious variations.
  • FGO trains multi-band mappings and progressively routes trajectories through sub-frequency manifolds with expanding spectral bands during reverse denoising.
  • FGO suppresses high-frequency noise during denoising and consistently outperforms counterparts in success rate and action smoothness across simulated and real-world evaluations.

2 Background

Diffusion policies generate action chunks by iteratively denoising Gaussian noise conditioned on observation history. DCT-based filtering decomposes action trajectories into frequency components and retains low-frequency components to form sub-frequency actions used by FGO.

  • Diffusion policies condition iterative action denoising on a history of observations and predict chunks of future actions.
  • Training perturbs clean action chunks with isotropic Gaussian noise, while the policy learns to predict that injected noise under a diffusion step.
  • During inference, the policy starts from pure Gaussian noise and performs K denoising iterations toward the manifold of noise-free actions.
  • DCT decomposes each time-domain action dimension into cosine basis functions with varying frequencies.
  • The low-pass filter retains the first f frequency components and reconstructs a frequency-truncated action chunk through the inverse DCT.
  • FGO’s forward process applies low-pass filters to full-frequency trajectories, mapping them onto corresponding sub-frequency manifolds before noise perturbation.

3 Frequency Guidance Operator (FGO)

FGO learns frequency-conditioned mappings from noise to sub-frequency manifolds and progressively guides reverse denoising toward the full-frequency manifold. Its training couples noise level and frequency selection, while inference approximates filtered noisy inputs when clean actions are unavailable.

  • 3.1 Learning Multi-Band Mappings from Noise to Data: FGO replaces direct broadband prediction with frequency-conditioned mappings from noise to specific sub-frequency manifolds.
  • 3.1 Learning Multi-Band Mappings from Noise to Data: Training applies a low-pass filter to action chunks and samples cut-off frequencies above a base threshold to preserve global kinematic structure.
  • 3.2 Progressive Guidance Toward the Full-Frequency Manifold: Reverse denoising traverses increasingly complex frequency manifolds using linear combinations of two conditional noise estimates at each diffusion step.
  • 3.2 Progressive Guidance Toward the Full-Frequency Manifold: The composite vector field interpolates a base-manifold estimate with an intermediate higher-cutoff estimate, while the cut-off frequency increases throughout reverse denoising.
  • 3.2 Progressive Guidance Toward the Full-Frequency Manifold: Because the clean action trajectory is unknown during reverse sampling, FGO approximates frequency-truncated noisy inputs by directly low-pass filtering the full-frequency noisy state.
  • 3.2 Progressive Guidance Toward the Full-Frequency Manifold: The sampling heuristic can introduce minor off-manifold deviations, although empirical evaluations report robustness and efficacy.
  • The training and sampling procedures specify frequency bases, schedules, guidance weights, and iterative updates for producing final actions.
  • 3.3 k-f Coupled (KFC) Sampling: KFC sampling dynamically adjusts the upper cut-off-frequency bound with noise level, restricting high-noise training to narrower low-frequency bands.

4 Experiments

FGO is evaluated across 15 robotic manipulation tasks spanning four simulation benchmarks and one real-world setup, using success, smoothness, computational-cost, and ablation analyses. It generally improves or matches task success, produces smoother actions, and introduces negligible training but higher inference overhead.

  • Experimental Setup: FGO is evaluated on 15 robotic manipulation tasks across four simulation benchmarks and one real-world setup.Simulation covers Robosuite, MimicGen, Adroit, and DexArt; the real-world evaluation uses an xArm manipulator.
  • Evaluation Metrics: Success rates are averaged over 3 training seeds and evaluated using the best checkpoint over 50 independent simulation episodes.The reported results use mean and standard deviation across seeds.
  • Simulation Benchmark Results: FGO outperforms all competitors on 3 of 4 Robosuite tasks, achieves the highest rates on both MimicGen tasks, and leads on 6 of 7 Adroit and DexArt tasks.It remains comparable to DP3 on the remaining task in each relevant benchmark grouping.
  • Action Smoothness: FGO achieves the lowest ATV and JerkRMS on the Robosuite Can approach phase, indicating smoother and more temporally consistent actions than the baselines.The metrics are computed over the first 32 time steps to avoid later divergence caused by task success or failure.
  • Computational Cost: FGO adds negligible training time relative to DP3 but has comparatively higher inference latency.The paper identifies this guidance-related inference overhead as a primary direction for future optimization.
  • Real-World Experiments: In real-world Cup and Mouse tasks, FGO consistently outperforms DP3 in success rate.Both tasks are deployed on an xArm manipulator with a two-finger gripper.
  • Ablations: Ablations show that removing explicit base-frequency sampling degrades performance on all three tasks, while interpolation guidance weights outperform extrapolation weights on Robosuite Lift.The standard configuration uses pbase = 0.2, KFC sampling, and linear inference schedules for fk and ωk.

5 Related Work

Prior work uses guidance to steer diffusion and flow-based generation, while frequency-domain analyses reveal distinct spectral biases in deep generative models.

  • Guidance methods steer diffusion and flow-based generation, including classifier guidance, classifier-free guidance, and robotics applications for observation or target-state adherence.
  • Classifier guidance trades sample diversity for visual quality, while classifier-free guidance removes the need for externally trained classifiers.
  • Robotics research has adapted guidance to diffusion policies and vision-language-action models to improve observation adherence, temporal consistency, and action coherence.
  • Frequency-domain analyses of GANs identify a spectral bias toward low-frequency global structures and difficulty synthesizing coherent high-frequency details.

6 Limitations

FGO adds inference-time computation and can occasionally oversmooth action trajectories, limiting responsiveness and precision in demanding manipulation settings.

  • FGO introduces additional inference-time computational overhead that can reduce kinematic responsiveness in tasks requiring high-frequency control loops.
  • FGO can occasionally generate over-smoothed action trajectories that are detrimental to fine-grained manipulation requiring high-precision action predictions.
  • The method therefore faces a trade-off between smoother guided denoising and responsiveness or precision in high-frequency control and fine-grained manipulation.

7 Conclusion

The paper presents FGO, which uses frequency-domain inductive biases and multi-band action mappings to guide reverse denoising through expanding sub-frequency manifolds. Experiments report state-of-the-art policy performance with improved action smoothness and temporal consistency.

  • FGO is a diffusion guidance paradigm that uses frequency-domain inductive biases to maneuver the reverse denoising process.
  • Training on low-pass-filtered action trajectories teaches multi-band mappings from noise to sub-frequency data manifolds.
  • During reverse denoising, a composite vector field progressively drives noisy samples toward the full-frequency manifold through expanding sub-frequency manifolds.
  • Extensive experiments validate state-of-the-art policy performance alongside significantly improved smoothness and temporal consistency of generated action trajectories.

A Derivation of Ak,f

The derivation defines frequency-truncated action states by applying low-pass filtering at a cutoff frequency and relates them to complementary high-pass filtering and noisy diffusion states.

  • A full-frequency action trajectory is represented together with its frequency-truncated counterpart.
  • The frequency-truncated trajectory is defined using a low-pass filter L_f at cutoff frequency f.
  • The same truncation can be expressed through the complementary high-pass filter H_f.
  • Substituting the filtering relation into forward diffusion expresses the frequency-truncated noisy state in terms of the full-frequency noisy state.

B Experimental Setup

The experiments span 15 tasks across four simulation benchmarks and one real-world platform, using varied robot embodiments, point-cloud observations, and standardized training and evaluation settings.

  • Task and Hardware Configurations: The evaluation covers 15 tasks across four simulation benchmarks and one real-world platform.The configurations include Robosuite, MimicGen, Adroit, DexArt, and a real-world setup.
  • Task and Hardware Configurations: Robosuite and MimicGen use a Franka Emika Panda with dual-viewpoint point clouds, while Adroit and DexArt use Shadow and Allegro Hands with single-viewpoint observations.
  • Real-World Setup: The real-world setup uses an xArm manipulator and a ZED 2 stereo camera in a tabletop workspace.The observation pipeline includes proprioception and processed third-person point clouds.
  • Real-World Setup: Expert demonstrations are collected by teleoperating the xArm with a Meta Quest 3 headset and spatial controllers.Controller poses are translated into end-effector targets, while triggers control the gripper.
  • Evaluation Protocol: Policies are evaluated over 25 randomized trials per real-world task, with episodes ending on success, unsafe collision, or a 50-step timeout.
  • Training and Implementation: FGO is integrated into DP3 using a lightweight MLP frequency encoder, while training uses 3,000 epochs on a single NVIDIA RTX 4090 GPU.Batch sizes are 512 for Robosuite and MimicGen and 128 for Adroit, DexArt, and real-world benchmarks.

E Supplementary Results

Supplementary comparisons show that generic guidance and post-hoc smoothing can improve smoothness but often reduce task success by amplifying atypical behavior, over-smoothing, or removing useful action details.

  • Alternative Guidance Methods: Adding classifier-free guidance to DP3 negatively affects 8 tasks, changes 1 negligibly, and improves success rates on 4 tasks.The authors associate this pattern with over-amplification of observation-specific behaviors and atypical low-probability actions.
  • Alternative Guidance Methods: Action coherence guidance paired with DiT-Policy broadly degrades performance, except on the DexArt Faucet and Bucket tasks.The proposed explanation is that rigid intra-chunk coherence corrupts fine-grained adjustments needed for completion.
  • Alternative Smoothing Methods: Low-pass filtering and temporal ensembling produce smoother actions with lower ATV and JerkRMS but reduce success rates on most tasks.
  • Alternative Smoothing Methods: Low-pass filtering removes fine-grained details alongside high-frequency noise, while temporal ensembling collapses multimodal predictions and induces contradictory control signals.

F Frequency Analysis

Frequency analysis shows that FGO progressively refines low-frequency trajectory structure while attenuating high-frequency components, producing lower intermediate high-frequency variance than DP3.

  • Frequency Evolution: FGO progressively refines low-frequency components into a smooth trajectory while driving high-frequency components toward zero during denoising.
  • Frequency Evolution: Compared with DP3, FGO generates trajectories with notably less high-frequency variance during intermediate denoising steps.
  • Figure 5: Figure 5 encodes denoising progression through color intensity, from light at k = K to dark at k = 0, comparing DP3 with FGO.
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