  In this paper we establish the correspondence between ghost-free bimetric
theory and a class of higher derivative gravity actions, including conformal
gravity and New Massive Gravity. We also characterize the relation between the
respective equations of motion and classical solutions. We illustrate that, in
this framework, the spin-2 ghost of higher derivative gravity is an artifact of
the truncation to a 4-derivative theory. The analysis also gives a relation
between the proposed partially massless (PM) bimetric theory and conformal
gravity, showing, in particular, the equivalence of their equations of motion
at the 4-derivative level. For the PM bimetric theory this provides further
evidence for the existence of an extra gauge symmetry and the associated loss
of a propagating mode away from de Sitter backgrounds. The new symmetry is an
extension of Weyl symmetry which also suggests the PM bimetric theory as a
ghost-free completion of conformal gravity.
