Question about Variational Autoencoders

I have a VAE and AE. Now I know that an AE is able to output a latent code (z), but a VAE outputs a latent code by sampling z from the mean and standard deviation vectors as, z = \mu + \epsilon*\sigma (reparameterization trick).

My question is that if it’s possible for the VAE to produce the same latent code (z) as the AE? What would happen if I set \epsilon = 0. Would it be the same latent …

code deeplearning deviation mean sampling standard vae variational autoencoders vectors