Regarding Spherical Gaussian Latent Space I am currently reading paper on Variational Autoencoders by Dr. Kingma and Dr. Welling, and am having a few confusions.

Question 1: What is a spherical Gaussian latent space? How do we interpret it
Question 2: In equation 1.15, does the Roman I in standard deviation mean 1 or does it have a different meaning?
Could anyone please provide me some information on these?

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*A spherical gaussian distribution is a multivariate normal distribution that has diagonal covariance and equal variances in all directions. A "spherical gaussian latent space" means that the latent space is a random variable with a spherical gaussian distribution.


*$I$ is the identity matrix.
