Training and sampling are different

During training, we compare real-data samples with generated samples and use an objective to update $\theta$. During ordinary sampling after training, $\theta$ stays fixed and new latent inputs produce new outputs. A comparison/update loop is a conceptual picture; it does not guarantee that every update reduces the divergence.

The chapter asks four connected questions: How can we measure mismatch without knowing the true density? Which divergence should we choose? Which generator family should we use? How can we optimize the parameters? These are design questions, not compulsory sequential stages.