Fig. 5.

Geometric view of deep generative models. Fixed distribution ζ in $\mathcal{Z}$ is pushed to μ_θ in $\mathcal{X}$ by the network G_θ, so that the mapped distribution μ_θ approaches the real distribution μ. In VAE, G_θ works as a decoder to generate samples, while F_ϕ acts as an encoder, additionally constraining ζ_ϕ to be as close to ζ. With such geometric view, auto-encoding generative models (e.g. VAE), and GAN-based generative models can be seen as variants of this single illustration.