In this work we employ the Bold Diagrammatic Monte Carlo method to establish the superfluid phase diagram of the two-dimensional Hubbard model in terms of density and interaction strength and for several values of next-nearest-neighbor hopping. We find that although a multitude of superfluid states persists up to moderate interactions the picture changes severely as compared to the weak-coupling interaction limit. We analyze how relative proximity to the Van Hove filling affects the leading effective Cooper pairing strengths and find that its influence rapidly diminishes with increasing interaction strength.