Reviews: Gaussian Process Conditional Density Estimation

This paper designs a model for conditional density estimation. It resembles a VAE architecture, where both x and y are given as inputs to the encoder to produce a latent variable w. W and x are then fed to the decoder to produce p(y x). However, unlike in VAE, x and y are not single data points, but rather sets and the decoder part uses GPs to output p(y x). I found the clarity of the paper very low and I wish authors explained the model in Section 3.1. Figure 1 made me especially confused as I initially thought that the model receives a single datapoint (x,y) just like a VAE.