  We introduce a new renormalization group theory to examine the quantum phase
transitions upon exiting the insulating phase of a disordered, strongly
interacting boson system. For weak disorder we find a direct transition from
this Mott insulator to the Superfluid phase. In d > 4 a finite region around
the particle-hole symmetric point supports this direct transition, whereas for
2=< d <4 perturbative arguments suggest that the direct transition survives
only precisely at commensurate filling. For strong disorder the renormalization
trajectories pass next to two fixed points, describing a pair of distinct
transitions; first from the Mott insulator to the Bose glass, and then from the
Bose glass to the Superfluid. The latter fixed point possesses statistical
particle-hole symmetry and a dynamical exponent z, equal to the dimension d.
