  Bilayer transition metal dichalcogenides (TMDs) belong to a class of
materials with two unique features, the coupled spin-valley-layer degrees of
freedom and the crystal structure that is globally centrosymmetric but locally
non-centrosymmetric. In this work, we will show that the combination of these
two features can lead to a rich phase diagram for unconventional
superconductivity, including intra-layer and inter-layer singlet pairings and
inter-layer triplet pairings, in bilayer superconducting TMDs. In particular,
we predict that the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state can
exist in bilayer TMDs under an in-plane magnetic field. We also discuss the
experimental relevance of our results and possible experimental signatures.
