Explains why GANs and VAEs avoid learning explicit data density
Shows the intractable integral behind latent-variable generative models
Sets up flow-based models as the tractable-density alternative
Key quotes
“Neither of them explicitly learns the probability density function of real data”
Transcript
So far, I’ve written about two types of generative models, GAN and VAE . Neither of them explicitly learns the probability density function of real data, $p(\mathbf{x})$ (where $\mathbf{x} \in \mathcal{D}$) — because it is really hard! Taking the generative model with latent variables as an example, $p(\mathbf{x}) = \int p(\mathbf{x}\vert\mathbf{z})p(\mathbf{z})d\mathbf{z}$ can hardly be calculated as it is intractable to go through all possible values of the latent code $\mathbf{z}$.
