  Motivated by recent experimental realization of a Bose-Einstein condensate
(BEC) of dipolar molecules, we develop superfluid transport theory for a
dissipative BEC to show that a weak uniform two-body loss can induce phase
rigidity, leading to superfluid transport of bosons. A generalized f-sum rule
is shown to hold for a dissipative superfluid as a consequence of weak U(1)
symmetry. It is also demonstrated that dissipation enhances the stability of a
molecular BEC with dipolar interactions. Possible experimental situations for
measuring the superfluid fraction and the spectral function are discussed.
