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 without repulsive interactions. A generalized $f$-sum rule is shown to hold for a dissipative superfluid as a consequence of weak U(1) symmetry. We also demonstrate that dissipation enhances the stability of a molecular BEC with dipolar interactions. Possible experimental signatures of dissipative superfluidity are discussed.

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• Bose-Einstein condensates
• Cold and ultracold molecules
• Dipolar gases
• Effective field theory
• Open quantum systems
• Superfluidity
• Linear response theory