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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.