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I know that the notation $\mathcal{N}(\mu, \sigma)$ stands for a normal distribution. But I'm reading the book "An Introduction to Variational Autoencoders" and in it, there is this notation: $$\mathcal{N}(z; 0, I)$$ What does it mean?

picture of the book: picture of the book An Introduction to Variational Autoencoders

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    – nbro
    Jan 10, 2021 at 15:54

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It means that $z$ has a (multivariate) normal distribution with 0 mean and identity covariance matrix. This essentially means each individual element of the vector $z$ has a standard normal distribution.

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    – nbro
    Jan 10, 2021 at 15:52

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