The posterior network and the prior network have the same structure and both output a probability distribution of latent variable z.
the only difference is that the input of the posterior network is the concatenation of the encoded definition x and the condition vector c while the input of the prior network is only the condition vector c. the output of the posterior network p = p α (z|d * , u, s) and the output of the prior network p = p β (z|u, s).