  We establish the zero-diffusion limit for both continuous and discrete
aggregation models over convex and bounded domains. Compared with a similar
zero-diffusion limit derived in [44], our approach is different and relies on a
coupling method connecting PDEs with their underlying SDEs. Moreover, our
result relaxes the regularity assumptions on the interaction and external
potentials and improves the convergence rate (in terms of the diffusion
coefficient). The particular rate we derive is shown to be consistent with
numerical computations.
