# Why using Aux() to implement VAE_1?

I have a bit of difficulties working on the article :https://arxiv.org/pdf/2009.07047v1.pdf. I want to implement the VAE_1, but it used VAE-GAN. I am familiar with VAE and GAN separetely, but a mixture of VAE-GAN looks quite challenging to implement. To better understand a VAE-GAN, I observe the link https://pravn.wordpress.com/category/vae-gan-vaegan/, but they used an auxiliary network called Aux(). I am not sure to understand the link with Aux() and what is in the article https://arxiv.org/pdf/2009.07047v1.pdf at the point Domain alignment in the VAE latent space. Do I have to use such auxiliary network to implement VAE_1?