FIG. 72.

VAEs learn a joint distribution p_θ(x, z) between latent variables z with prior distribution p(z) and data x. The conditional distribution p_θ(x|z) can be thought of as a stochastic “decoder” that maps latent variables to new examples. The stochastic “encoder” q_ϕ(z|x) approximates the true but intractable p_θ(z|x) – much like mean-field theories in statistical physics approximate true distributions with analytically tractable approximations. Figure based on Kingma’s Ph.D. dissertation Chapter 2. (Kingma et al., 2017).