  We demonstrate that quantum coherence can be generated by the interplay of
coupling to an incoherent environment and kinetic processes. This joint effect
even occurs in a repulsively interacting fermionic system initially prepared in
an incoherent Mott insulating state. In this case, coupling a dissipative noise
field to the local spin density produces coherent pairs of fermions. The
generated pair coherence extends over long distances as typically seen in
Bose-Einstein condensates. This conceptually surprising approach provides a
novel path towards a better control of quantum many-body correlations.
