We test if the cosmological zoom-in simulations of isolated galaxies from the FIRE project reproduce the properties of ultra diffuse galaxies. We show that stellar feedback-generated outflows that dynamically heat galactic stars, together with a passively aging stellar population after imposed quenching (from e.g. infall into a galaxy cluster), naturally reproduce the observed population of red UDGs, without the need for high spin halos or dynamical influence from their host cluster. We reproduce the range of surface brightness, radius and absolute magnitude of the observed z=0 red UDGs by quenching simulated galaxies at a range of different times. They represent a mostly uniform population of dark matter-dominated galaxies with M_star ~1e8 Msun, low metallicity and a broad range of ages. The most massive simulated UDGs require earliest quenching and are therefore the oldest. Our simulations provide a good match to the central enclosed masses and the velocity dispersions of the observed UDGs (20-50 km/s). The enclosed masses of the simulated UDGs remain largely fixed across a broad range of quenching times because the central regions of their dark matter halos complete their growth early. A typical UDG forms in a dwarf halo mass range of Mh~4e10-1e11 Msun. The most massive red UDG in our sample requires quenching at z~3 when its halo reached Mh ~ 1e11 Msun. If it, instead, continues growing in the field, by z=0 its halo mass reaches > 5e11 Msun, comparable to the halo of an L* galaxy. If our simulated dwarfs are not quenched, they evolve into bluer low-surface brightness galaxies with mass-to-light ratios similar to observed field dwarfs. While our simulation sample covers a limited range of formation histories and halo masses, we predict that UDG is a common, and perhaps even dominant, galaxy type around Ms~1e8 Msun, both in the field and in clusters.

20 pages, 13 figures; match the MNRAS accepted version