Like most galaxies, the Milky Way harbors a supermassive black hole (SMBH) at its center, surrounded by a nuclear star cluster. In this dense star cluster, direct collisions can occur between stars before they evolve off the main sequence. Using a statistical approach, we characterize the outcomes of these stellar collisions within the inner parsec of the Galactic center (GC). Close to the SMBH, where the velocity dispersion is larger than the escape speed from a Sun-like star, collisions lead to mass loss. We find that the stellar population within 0.01 pc is halved within about a billion years because of destructive collisions. Additionally, we predict a diffuse population of peculiar low-mass stars in the GC. These stars have been divested of their outer layers in the inner 0.01 pc before migrating to larger distances from the SMBH. Between 0.01 and 0.1 pc from the SMBH, collisions can result in mergers. Our results suggest that repeated collisions between lower-mass stars can produce massive (≳10 M
⊙) stars, and that there may be ∼100 of them residing in this region. We provide predictions on the number of so-called G objects, dust- and gas-enshrouded stellar objects, that may result from main-sequence stellar collisions. Lastly, we comment on uncertainties in our model and possible connections between stellar collisions and the missing red giants in the GC.