  The highly unusual divalent silver in silver difluoride (AgF$_2$) features a
nearly square lattice of Ag$^{+2}$ bridged by fluorides. As a structural and
electronic analogue of cuprates, its superconducting properties are yet to be
examined. Our first principles electronic structure calculations reveal a
striking resemblance between AgF$_2$ and the cuprates. Computed spin
susceptibility shows a magnetic instability consistent with the experimentally
observed antiferromagnetic transition. A linearized Eliashberg theory in
fluctuation-exchange approximation shows an unconventional singlet $d$-wave
superconducting pairing for bulk AgF$_2$ at an optimal electron doping. The
pairing is found to strengthen with a decreasing interlayer coupling,
highlighting the importance of quasi-2D nature of the crystal structure. These
findings place AgF$_2$ in the category of unconventional high-$T_\text{C}$
superconductors, and its chemical uniqueness may help shed new lights on the
high-$T_\text{C}$ phenomena.
