-Given a training set $x_1, \dots, x_N$ that follows an unknown
-distribution $\mu_X$, we want to fit a model $p_\theta(x,z)$ to it,
-maximizing
+Given a training i.i.d train samples $x_1, \dots, x_N$ that follows an
+unknown distribution $\mu_X$, we want to fit a model $p_\theta(x,z)$
+to it, maximizing