  In nonperturbative regimes, the superfluid instability in the two-dimensional
Hubbard model can be described by an emergent BCS theory with small effective
pairing constants. We compute the effective couplings using a controlled
bold-line diagrammatic Monte Carlo approach, which stochastically sums all
skeleton Feynman diagrams dressed in the one- and two-particle channels to high
expansion orders, and map out the resulting superfluid ground-state phase
diagram in a range of next-nearest-neighbor hopping $0 \leq t^{\prime} \leq
0.3t$, interaction strength $0 \leq U \leq 3t$, and lattice filling $0 \leq n
\leq 2$. The phase diagram is dramatically transformed in the hole-doped region
and becomes particularly rich at larger doping and $t'$. At $t'=0.3$, the
weak-coupling picture with the dominant triplet pairing sharply peaked at $n
\approx 0.73$ due to the Van Hove singularity is replaced by a plateau of the
singlet $d_{x^2-y^2}$ paring, while for $U \gtrsim 3t$ the effective couplings
are consistent with the $d_{x^2-y^2}$ high-temperature superconductivity in the
hole-doped region near cuprates' optimal doping.
