If we have $\mu$ mean and symmetric covariance matrix C in 2D they are defined as: $\mu$ = $\begin {bmatrix} \mu_1 \\ \mu_2 \\ \end {bmatrix}$

$C$ = $\begin {bmatrix} \sigma_{1}^{2} & r \sigma_1 \sigma_2 \\ r \sigma_1 \sigma_2 & \sigma_{2}^{2}\\ \end {bmatrix}$

In Variational AutoEncoder is assumed that there is no correlation between these dimensions. This means that encoder needs to map each input to mean and variance vectors. So, as the result image will be encoded into two vectors:

1. mu - the mean point distribution.
2. log_var - the logarithm of the variance of each dimensions. In order to encode image into a specific point we can use this formula: $z = mu + exp(log\_var / 2)$