We study the model theory of expansions of Hilbert spaces by generic
predicates. We first prove the existence of model companions for generic
expansions of Hilbert spaces in the form first of a distance function to a random
substructure, then a distance to a random subset. The theory obtained with the
random substructure is {\omega}-stable, while the one obtained with the distance
to a random subset is $TP_2$ and $NSOP_1$. That example is the first continuous
structure in that class.