VAE requires the standard Gaussian distribution as a prior in the latent space. Since all codes tend to follow the same prior, it often suffers the so-called posterior collapse. To avoid this, this paper introduces the class specific distribution for the latent code. But different from CVAE, we present a method for disentangling the latent space into the label relevant and irrelevant dimensions, $bm{mathrm{z}}_s$ and $bm{mathrm{z}}_u$, for a single input. We apply two separated encoders to map the input into $bm{mathrm{z}}_s$ and $bm{mathrm{z}}_u$ respectively, and then give the concatenated code to the decoder to reconstruct the input. The label irrelevant code $bm{mathrm{z}}_u$ represent the common characteristics of all inputs, hence they are constrained by the standard Gaussian, and their encoder is trained in amortized variational inference way, like VAE. While $bm{mathrm{z}}_s$ is assumed to follow the Gaussian mixture distribution in which each component corresponds to a particular class. The parameters for the Gaussian components in $bm{mathrm{z}}_s$ encoder are optimized by the label supervision in a global stochastic way. In theory, we show that our method is actually equivalent to adding a KL divergence term on the joint distribution of $bm{mathrm{z}}_s$ and the class label $c$, and it can directly increase the mutual information between $bm{mathrm{z}}_s$ and the label $c$. Our model can also be extended to GAN by adding a discriminator in the pixel domain so that it produces high quality and diverse images.
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