The calculation of NMSE is not changing even after changing the latent dimension from 512 to 32
the normalized mean square error values should change after changing the latent dimension.
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Variational autoencoder is different from autoencoder in a way such that it provides a statistic manner for describing the samples of the dataset in latent space. Therefore, in variational autoencoder, the encoder outputs a probability distribution in the bottleneck layer instead of a single output value.
Variational autoencoders were originally designed to generate simple synthetic images. Since their introduction, VAEs have been shown to work quite well with images that are more complex than simple 28 x 28 MNIST images. For example, it is possible to use a VAE to generate very realistic looking images of people.
