  We study hybrid atom-molecule quantum walks in one-dimensional optical
lattices with two interacting bosonic atoms which may be converted into a
molecule. The hybrid atom-molecule energy bands include a continuum band and
two isolated bands, which respectively correspond to scattering states and
dressed bound states (DBS's). Because of the atom-molecule coupling, the DBS's
may appear even in the absence of atom-atom interaction. From an initial state
of two atoms occupying the same site, in addition to independent quantum walks
which correspond to scattering states, correlated quantum walks appear as a
signature of DBS's. Even if the atom-atom interaction and the atom-molecule
coupling are much stronger than the tunneling strengths, independent quantum
walks may still appear under certain resonant conditions. The correlated
quantum walks show two light-cones with different propagation velocities, which
can be analytically explained by the effective tunneling strengths of the two
different DBS's. Furthermore, the effective nearest-neighbor tunneling of DBS's
can be suppressed to zero, which can be explained by the destructive
interference between the atomic pair and the molecule.
