FODMP: Fast One-Step Diffusion of Movement Primitives Generation for Time-Dependent Robot Actions

1. Problem Statement

The paper addresses a critical trade-off in current diffusion-based robot learning policies: Speed vs. Expressiveness.

• Action-Chunking Policies (e.g., ManiCM): These predict short sequences of actions (chunks) in a single step. They are fast and suitable for real-time control but lack temporal structure. They cannot generate complex, time-dependent motion primitives (e.g., specific acceleration/deceleration profiles required for catching a ball) and are inherently reactive rather than anticipatory.
• Movement Primitive Diffusion (MPD): This approach uses Probabilistic Dynamic Movement Primitives (ProDMPs) to parameterize full trajectories, capturing rich temporal structures. However, it relies on multi-step denoising (typically 10–50 steps) to infer parameters, resulting in prohibitively high inference latency. This makes MPD unsuitable for closed-loop, real-time control.

The Gap: There is a lack of a method that can generate structured, time-dependent motion primitives with the inference speed required for real-time robotic control.

2. Methodology: FODMP

The authors propose FODMP (Fast One-Step Diffusion of Movement Primitives), a framework that unifies the temporal expressiveness of ProDMPs with the efficiency of one-step diffusion via Consistency Distillation.

Core Components:

1. Trajectory Representation (ProDMPs):
   Instead of predicting raw action sequences, the model predicts the parameters ($\theta = [w, g]$) of Probabilistic Dynamic Movement Primitives.

   • $w$: Forcing weights shaping the trajectory.
   • $g$: Attractor ensuring convergence to the goal.
   • These parameters encode entire time-dependent motion profiles (including acceleration and deceleration phases) without requiring numerical integration during inference.

2. Teacher-Student Distillation Pipeline:

   • Teacher Model: A standard multi-step diffusion model (based on MPD) trained to denoise ProDMP parameters over $K$ steps. It serves as the "ground truth" for temporal consistency but is too slow for deployment.
   • Student Model: A one-step diffusion model trained to map noisy parameters directly to clean parameters in a single inference step.
   • Consistency Distillation: The student is trained using a consistency loss. It learns to map a noisy input at step $t$ to the same clean output as the teacher would produce after $k$ steps of denoising. This is enforced using an Exponential Moving Average (EMA) target network.

3. Inference Process:

   • Sample noise $\theta_T \sim \mathcal{N}(0, I)$.
   • The student network $f_\phi$ directly predicts the clean ProDMP parameters $\theta_0$ in one step conditioned on observations (images, states).
   • A ProDMP decoder (ODE solver) converts $\theta_0$ into a smooth, continuous trajectory for the robot.

3. Key Contributions

• First One-Step Diffusion for Movement Primitives: FODMP is the first framework to combine consistency distillation with ProDMPs, enabling the generation of temporally expressive primitives at control-rate speeds.
• Breaking the Speed-Accuracy Trade-off: It eliminates the inference bottleneck of multi-step MPD while retaining the ability to model complex dynamic behaviors (like spring-damper profiles) that action-chunking policies miss.
• Real-World Validation: The method is validated not only on simulation benchmarks but also on challenging real-world tasks requiring high-speed, dynamic interception.

4. Experimental Results

A. Simulation Benchmarks (MetaWorld & ManiSkill)

• Success Rate: FODMP achieved the highest average success rate (78.2%), outperforming MPD (64.1%), standard Diffusion Policy (DP, 50.1%), and ManiCM (34.4%). It showed significant gains in "Medium" and "Hard" tasks requiring structured motion.
• Inference Speed: FODMP runs at 17.2 ms/step.
  • ~10x faster than MPD (168.6 ms).
  • ~7x faster than action-chunking policies like DP (119.7 ms).
  • This speed enables true closed-loop control.

B. Real-World Experiments

1. Push-T Task (Precision Manipulation):

   • FODMP outperformed baselines by 9.2% to 23.6% in success rate.
   • It demonstrated superior data efficiency, achieving high performance with fewer demonstrations compared to baselines that suffered from accumulated errors due to temporally unstable actions.

2. Ball Catching Task (Dynamic Interception):

   • This task required the robot to intercept a fast-moving ball, demanding precise acceleration/deceleration profiles.
   • Result: FODMP achieved a 68.2% higher success rate than DP and significantly outperformed MPD and ManiCM.
   • Qualitative: Baseline methods failed to catch the ball due to latency or jerky motion. FODMP generated smooth, anticipatory trajectories that successfully intercepted and stabilized the ball.

5. Significance and Impact

• Enabling Dynamic Skills: FODMP bridges the gap between high-level planning and low-level control, allowing robots to perform skills that require temporal anticipation (e.g., catching, fast assembly) rather than just reactive stepping.
• Scalability for Embodied AI: By decoupling the "action expert" (the one-step decoder) from the vision-language backbone, FODMP can be integrated into large-scale Vision-Language-Action (VLA) models (like $\pi_0$). This allows future foundation models to generate scalable, structured motions without the latency penalty of traditional diffusion.
• Practical Deployment: The reduction in inference latency from ~170ms to ~17ms makes diffusion models viable for high-frequency, closed-loop control loops in real-world robotics, a prerequisite for safe and effective human-robot interaction.

In summary, FODMP successfully distills the complex temporal reasoning of multi-step diffusion into a single-step process, providing a practical solution for generating high-quality, time-dependent robot actions in real-time.