−∇f(x)=argminv∈Rd{⟨∇f(x),v⟩+12‖v‖2} Thus, gradient flow is a greedy method in continuous time that flows following the (locally-optimal) steepest descent direction. In particular, gradient flow is a descent method, which means it always decreases the objective function: ddtf(Xt)=⟨∇f(Xt),˙Xt⟩=−‖∇f(Xt)‖2≤0.

A 'Deep Generative Model' is a type of generative model that aims to learn the joint probability of multiple variables and calculate the conditional posterior probability. It models the distribution of each class and can address data scarcity and data imbalance problems in tasks like video anomaly detection.