White dwarfs (WDs) embedded in gaseous disks of active galactic nucleus (AGNs) can rapidly accrete materials from the disks and grow in mass to reach or even exceed the Chandrasekhar limit. Binary WD (BWD) mergers are also believed to occur in AGN accretion disks. We study observational signatures from these events. We suggest that mass-accreting WDs and BWD mergers in AGN disks can lead to thermonuclear explosions that drive an ejecta shock breakout from the disk surface and power a slow-rising, relatively dim Type Ia supernova (SN). Such SNe Ia may be always outshone by the emission of the AGN disk around the supermassive black hole (BH) with a mass of $M_{rm SMBH}gtrsim 10^8,M_odot$. Besides, accretion-induced collapses (AICs) of WDs in AGN disks may occur sometimes, which may form highly-magnetized millisecond neutron stars (NSs). The subsequent spin-down process of this nascent magnetar can deposit its rotational energy into the disk materials, resulting in a magnetar-driven shock breakout and a luminous magnetar-powered transient. We show that such an AIC event could power a rapidly evolving and luminous transient for a magnetic field of $Bsim10^{15},{rm G}$. The rising time and peak luminosity of the transient, powered by a magnetar with $Bsim10^{14},{rm G}$, are predicted to have similar properties with those of superluminous supernovae. AIC events taking place in the inner parts of the disk around a relatively less massive supermassive BHs ($M_{rm SMBH}lesssim10^8,M_odot$) are more likely to power the transients that are much brighter than the AGN disk emission and hence easily to be identified.
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