Hello, I have a question about a conditional VAE model (CVAE model).

My CVAE model generates a 2D-sample (x,y), (=data, X) in a grid map.

The latent space (=z) dimension is 2, and the dimension of the conditional features (grid map features) is 8. The conditional features are an embedded grid map by CNN.

It runs well as I expected at test environments

Here is my question.

Is it OK with setting the latent space dimension (=z) as the same as the data dimension (=X)?

As I know, the objective of the VAE model is ‘to generate something with sampled latent vector’, not to reduce the dimension of data (=X), such as AE.

Or is there any other theoretic assumption that I need to set latent space dimension is lower than data dimension?

Thanks,