In this post, we will try to connect Energy-Based Model with classical optimal control frameworks like Model-Predictive Control from the perspective of Lagrangian optimization.

In this note we connect the energy concepts including Lagrangian Dynamics and Gibbs Formula to measuring the quality of prediction. Then we go over the inferencing and training in multi-modal scenarios.

In short, using diffusion process instead of directly applying MSE loss on trajectories enables a wider variety of trajectory solutions learnt from imitation data, instead of the trajectory provided by dataset(s), which is beneficial for small-set imitation learning. In this blog post, we will discuss how and why diffusion process can achieve such and trajectory-agnostic result.