Normalizing a Function to Create a Probability Distribution

A machine learning model is being trained to generate outputs. Its behavior is described by a probability distribution p_model(y|x), and the desired behavior is captured by a target data distribution p_data(y|x). The training process involves minimizing an objective function. Which of the following objective function structures is most desirable because it can be clearly interpreted as a measure of the 'distance' or difference between the two distributions?

Critique of an Objective Function Formulation

Evaluating Objective Function Designs