  We model the mass accretion rate $\dot{M}$ to stellar mass $M_*$ correlation
that has been inferred from observations of intermediate to upper mass T Tauri
stars---that is $\dot{M} \propto M_*^{1.3 \pm 0.3}$. We explain this
correlation within the framework of quiescent disk evolution, in which
accretion is driven largely by gravitational torques acting in the bulk of the
mass and volume of the disk. Stresses within the disk arise from the action of
gravitationally driven torques parameterized in our 1D model in terms of
Toomre's $Q$ criterion. We do not model the hot inner sub-AU scale region of
the disk that is likely stable according to this criterion, and appeal to other
mechanisms to remove or redistribute angular momentum and allow accretion onto
the star. Our model has the advantage of agreeing with large-scale
angle-averaged values from more complex nonaxisymmetric calculations. The model
disk transitions from an early phase (dominated by initial conditions inherited
from the burst mode of accretion) into a later self-similar mode characterized
by a steeper temporal decline in $\dot{M}$. The models effectively reproduce
the spread in mass accretion rates that have been observed for protostellar
objects of $0.2\,\mbox{M}_\odot \le M_* \le 3.0\,\mbox{M}_\odot$, such as those
found in the $\rho$ Ophiuchus and Taurus star forming regions. We then compare
realistically sampled populations of young stellar objects produced by our
model to their observational counterparts. We find these populations to be
statistically coincident, which we argue is evidence for the role of
gravitational torques in the late time evolution of quiescent protostellar
disks.
