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 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.

ScoreGrad is a EBM make use of iterative conditional SDE sampling via diffusion to perform multi-variate probabilistic time series prediction. Basically it uses RNN/LSTM/GRU to encode past time series as a condition and sample a probability distribution of predicting time series based on this.