The relationship between the pseudogap and underlying ground-state phases has not yet been rigorously established. We investigated the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations, allowing for the computation of spectral properties in the infinite-size limit and with arbitrary momentum resolution. We found three distinct regimes as a function of doping and interaction strength: a weakly correlated metal, a correlated metal with strong interaction effects, and a pseudogap regime at low doping. We show that the pseudogap forms both at weak coupling, when the magnetic correlation length is large, and at strong coupling, when it is shorter. As the temperature goes to zero, the pseudogap regime extrapolates precisely to the ordered stripe phase found by ground-state methods.