  We calculate the bulk-diffusion coefficient and the conductivity in a broad
class of conserved-mass aggregation processes on a ring of discrete sites.
These processes involve chipping and fragmentation of masses, which diffuse
around and aggregate upon contact with their neighboring masses. We find that,
even in the absence of microscopic time reversibility, the systems satisfy an
Einstein relation, which connects the ratio of the conductivity and the
bulk-diffusion coefficient to mass fluctuation. Interestingly, when aggregation
dominates over chipping, the conductivity or, equivalently, the mobility, gets
enhanced. The enhancement in conductivity, in accordance with the Einstein
relation, results in large mass fluctuations, implying a {\it mobility driven
clustering} in the system. Indeed, in a certain parameter regime, we
demonstrate that the conductivity diverges beyond a critical density, signaling
the onset of a condensation transition observed in the past. In a striking
similarity to Bose-Einstein condensation, the condensate formation along with
the diverging conductivity thus underlies a dynamic "superfluidlike" transition
in these nonequilibrium systems. Notably, the bulk-diffusion coefficient
remains finite in all cases. Our analytic results are in a quite good agreement
with simulations.
