sampling

Given a mean (vector) $\mu$ and a standard deviation (vector) $\sigma$, and a (vector of) noise $z$ from a spherical standard gaussian $z\sim \mathcal{N}(0,I)$, we can sample from the gaussian with mean $\mu$ and standard deviation $\sigma$ by scaling and shifting the noise:

$$x=\mu +\sigma \odot z$$

where $\odot$ denotes the element-wise product.
This is also called the reparametrization trick.