  We generalize the theory of flow equations to open quantum systems focusing
on Lindblad master equations. We introduce and discuss three different
generators of the flow that transform a linear non-Hermitian operator into a
diagonal one. We first test our dissipative flow equations on a generic matrix
and on a physical problem with a driven-dissipative single fermionic mode. We
then move to problems with many fermionic modes and discuss the interplay
between coherent (disordered) dynamics and localized losses. Our method can
also be applied to non-Hermitian Hamiltonians.
