Energy-Score Stabilized Attentive Mixture-Density Policy: A Lightweight Approach to Multimodal Robot Motion

For practical motion generation, it is essential to handle multimodality (multiple actions can be correct for the same observation) while maintaining low inference cost and strong generalization from limited demonstrations. We introduce an attentive mixture-density policy trained with the Energy Score that represents future visuomotor trajectories as explicit probability distributions with a single forward pass. Concretely, we output Gaussian mixture parameters for joint commands (and optionally attention points) and optimize them with the Energy Score (computed as a sum of 1D CRPS under a diagonal covariance assumption) instead of the negative log-likelihood (NLL) to avoid MDN singularities and gradient-scale instabilities. Our architecture couples explicit spatial attention with mixture-density outputs, enabling robust multimodal behavior selection under visual noise and small-data regimes. On an 8-DOF manipulator, the method generates distinct avoidance trajectories and stabilizes learning in obstacle avoidance. Moreover, in a randomized moving-object grasping task, where spatiotemporal multimodality and fast timing decisions are required, the proposed model outperforms Diffusion Policy by 15-25% under several unseen conditions, demonstrating superior generalization and real-time feasibility.