A significant fraction of the massive star-forming galaxies at high redshift are found to be gravitationally unstable disks with giant clumps. We present a simple theoretical framework in which the properties of disk galaxies can be studied in terms of gravitational instability and its relation to the cosmic web. An earlier analysis (see Dekel, Sari & Ceverino 2009) assumed pure gaseous disks and led to the tentative conclusion that an originally unstable disk remains unstable also at later times. This fails to account for the observed stable disks at low redshift. We now analyze the instability of a two-component disk where the gas continuously turns into stars. This allows us to follow the evolution of disk galaxies from high redshifts to today. Under the assumption that a galaxy disk maintains itself in a marginally unstable configuration, we study how different evolution paths for the stellar velocity dispersion result in different responses of the gas. We seek a self-consistent solution where the instability is self-regulated at marginal instability and where the gas pressure is larger than just its thermal component. We find that when the stellar velocity dispersion is increased because of the gravitational inflow to the disk center, the disk stabilizes by z~1. A similar stabilization is achieved when mass accretion onto the disk is assumed to happen, at least in part, through massive dense clumps rather than solely through smooth flows.