The increasing abundance of passive red-sequence galaxies since z=1-2 is mirrored by a coincident rise in the number of galaxies with spheroidal morphologies. In this paper, however, we show that in detail the correspondence between galaxy morphology and color is not perfect, providing insight into the physical origin of this evolution. Using the COSMOS survey, we study a significant population of red sequence galaxies with disk-like morphologies. These passive disks typically have Sa-Sb morphological types with large bulges, but they are not confined to dense environments. They represent nearly one-half of all red-sequence galaxies and dominate at lower masses (log Mstar < 10) where they are increasingly disk-dominated. As a function of time, the abundance of passive disks with log Mstar < 11 increases, but not as fast as red-sequence spheroidals in the same mass range. At higher mass, the passive disk population has declined since z~1, likely because they transform into spheroidals. We estimate that as much as 60% of galaxies transitioning onto the red sequence evolve through a passive disk phase. The origin of passive disks therefore has broad implications for understanding how star formation shuts down. Because passive disks tend to be more bulge-dominated than their star-forming counterparts, a simple fading of blue disks does not fully explain their origin. We explore several more sophisticated explanations, including environmental effects, internal stabilization, and disk regrowth during gas-rich mergers. While previous work has sought to explain color and morphological transformations with a single process, these observations open the way to new insight by highlighting the fact that galaxy evolution may actually proceed through several separate stages.
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