If you want to create VAE architecture except NN, you should watch this page!
This is a description of VAE with CNN (in Japanese): https://qiita.com/icchi-ioo/items/f24c392e09f22953d179
here is a basic description of VAE (in Japanse) : https://qiita.com/icchi-ioo/items/9d3d27106dc474cfdf1e