  Spin-orbit coupling in transition metal dichalcogenides (TMDCs) causes
spin-valley locking giving rise to unconventional optical, transport, and
superconducting properties. In this paper, we propose exotic superconductivity
in bilayer group-IV TMDCs by symmetry control. The sublattice-dependent hidden
spin-orbit coupling arising from local inversion symmetry breaking in the
crystal structure may stabilize the odd-parity superconductivity by purely
$s$-wave local pairing interaction. The stability of the odd-parity
superconducting state depends on the bilayer stacking. The 2H$_b$ stacking in
MoX$_2$ and WX$_2$ (X =S, Se) favors the odd-parity superconductivity due to
interlayer quantum interference. On the other hand, the odd-parity
superconductivity is suppressed by the 2H$_a$ stacking of NbSe$_2$. Calculating
the phase diagram of the tight-binding model derived from first principles band
calculations, we conclude that the intercalated bilayer MoS$_2$ and WS$_2$ are
candidates for a new class of odd-parity superconductors by spin-orbit
coupling.
