We study the random geometry approach to the $T \bar T$ deformation of $2d$ conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the $T \bar T$ deformation becomes a straightforward translation of the field theory language. Namely, the dual geometry is an ensemble of $AdS_3$ spaces or BTZ black holes, without a finite cutoff, but instead with randomly fluctuating boundary diffeomorphisms. This reflects an increase in degrees of freedom in the renormalization group flow to the UV by the irrelevant $T \bar T$ operator.