a fixed vector so that different $z$ could be chosen from the distribution to obtain different outputs $x$.

The VAE model could be modified to be conditioned on a certain attribute $c$ such as dialogue contexts to generate outputs given a source pattern. And such modification leads the original VAE to conditional VAE called CVAE [@yan2016attribute2image; @sohn2015learning]. Needless to say, the output of CVAE now depends both on $z$ and $c$ and the ELBO becomes: $$\begin{gathered}
{\log{p(x|c)}}\nonumber \\
\geq{\mathbb{E}_{q(z|x,c)}[\log{p(x|z,c)}]-KL(q(z|x,c)||p(z|c))}\label{cvae_elbo}\end{gathered}$$

VAE and CVAE seem to show great potential to generate diverse outputs, as the latent variable $z$ from a distribution could be modulated to help model different patterns. Some image generating tasks adopt VAE or CVAE and achieve good generative quality. In spite of this, difficulties are encountered while researchers attempted to generate texts via such structures [@bowman2016generating]. Directly optimized with Equation \[vae\_elbo\] or Equation \[cvae\_elbo\] will lead to the *KL-Vanishing problem* which is also called as the *posterior collapse problem*. For the VAE model, the encoder $q_{\phi}(z|x)$ perfectly fits the prior distribution $p(z)$ while ignores the inputs and the decoder generates outputs without referring to $z$. Same problems take place all conditioned on $c$ while CVAE is used.

[@bowman2016generating] presented 