explicit objective. Nevertheless, it is hard to find an appropriate trade-off point.

Self Labeling CVAE
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Our goal is to generate diverse $x$ using different $z$. From the perspective of the decoder, two conditions should be satisfied: First, each $z$ should correspond to a unique $x$ through the decoder. Second, $z$ should obey the prior distribution $p(z)$. Maximizing the ELBO objective encourages the latter by pulling encoder’s output distribution of $z$ to $p(z)$. However, with the $p(z|x)$ moving towards $p(z)$ during the optimizing procedure, $z$ losses the discriminative information and the decoder tends to fit the data even without the help of encoders. As a consequence, the first condition is violated and multiple $z$s will collapse to a same averaged output distribution $p(x)$, as is shown in Fig. \[fig:latentspace\](b).

Thus we propose to strengthen the connection between the latent $z$ and target $x$ via maintaining the expressiveness of the encoder. As illustrated in Fig. \[fig:latentspace\](a), considering that an expressive $z$ has the ability to recover a unique target through the decoder, the decoder itself can then be used to find the most expressive $z'$ given a certain target $x$. This in concept equivalents to find the inverse image of $x$ 