While accreting through a circumstellar disk, young stellar objects are observed to undergo sudden and powerful accretion events known as FUor or EXor outbursts. Although such episodic accretion is considered to be an integral part of the star formation process, the triggers and mechanisms behind them remain uncertain. We conducted global numerical hydrodynamics simulations of protoplanetary disk formation and evolution in the thin-disk limit, assuming both magnetically layered and fully magnetorotational instability (MRI)-active disk structure. In this paper, we characterize the nature of the outbursts occurring in these simulations. The instability in the dead zone of a typical layered disk results in “MRI outbursts.” We explore their progression and their dependence on the layered disk parameters as well as cloud core mass. The simulations of fully MRI-active disks showed an instability analogous to the classical thermal instability. This instability manifested at two temperatures—above approximately 1400 K and 3500 K—due to the steep dependence of Rosseland opacity on the temperature. The origin of these thermally unstable regions is related to the bump in opacity resulting from molecular absorption by water vapor and may be viewed as a novel mechanism behind some of the shorter duration accretion events. Although we demonstrated local thermal instability in the disk, more investigations are needed to confirm that a large-scale global instability will ensue. We conclude that the magnetic structure of a disk, its composition, as well as the stellar mass, can significantly affect the nature of episodic accretion in young stellar objects.