Recent infrared surveys have shown that the luminosity functions of protostars peak near one solar luminosity, and have a larger fraction of objects at sub-solar luminosities, which seem too low given the need to accrete the central protostar in typical estimated lifetimes. One plausible solution to this “luminosity problem'' is that mass infall occurs first to the disk, and subsequent disk accretion is low for the most of the time, with occasional short-lived, rapid accretion outbursts. In this talk I will present our recent numerical results of gravitational instability (GI)-induced, magnetorotational instability (MRI)-driven accretion outbursts in protoplanetary disks. Our results emphasize the importance of following the propagation of mass into innermost disk radii for predicting the resulting accretion luminosity as a function of time and thus addressing the protostellar luminosity problem.