Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generation

Robotic manipulation policies often rely on generating discrete 'action chunks'—sequences of actions executed at fixed frequencies. However, this discretization creates two major problems: it fails to handle training data collected at heterogeneous frequencies (leading to gradient conflicts) and it produces temporally inconsistent, jittery motions that can be detrimental in sensitive tasks like soft-body manipulation or surgery. This paper asks how to generate continuous, temporally consistent actions that remain robust to varying input frequencies.

The authors introduce Frequency-Aware Flow Matching (FAFM). Instead of predicting discrete action steps, FAFM transforms demonstration trajectories into the frequency domain using the Discrete Cosine Transform (DCT). By performing flow matching on these DCT coefficients, the model learns a continuous representation that can be reconstructed at any temporal resolution. To ensure temporal consistency, the authors add a regularization term that penalizes the first-order temporal derivative of the predicted actions. This effectively acts as a Sobolev-type constraint, suppressing high-frequency noise and abrupt changes in the robot's motion.

FAFM demonstrates significant improvements across several benchmarks, including synthetic toy tasks, obstacle avoidance, LapGym (a surgical simulation), and the LIBERO benchmark for vision-language-action models. Key results include:

• Robustness: By using frequency-domain coefficients, the model resolves identifiability failures caused by mixed-frequency training data.
• Smoothness: The derivative-based regularization significantly improves motion smoothness, as measured by log dimensionless jerk (LDLJ).