  It is a well known result that any formulation of unimodular gravity is
classically equivalent to General Relativity (GR), however a debate exists in
the literature about this equivalence at the quantum level. In this work, we
investigate the UV quantum structure of a diffeomorphism invariant formulation
of unimodular gravity using functional renormalisation group methods in a
Wilsonian context. We show that the effective action of the unimodular theory
acquires essentially the same form with that of GR in the UV, as well as that
both theories share similar UV completions within the framework of the
asymptotic safety scenario for quantum gravity. Furthermore, we find that in
this context the unimodular theory can appear to be non--predictive due to an
increasing number of relevant couplings at high energies, and explain how this
unwanted feature is in the end avoided.
