We study a family of interacting particle diffusions that converge to their random ensemble-average at some fixed future time for any given number of elements in the system. We impose certain conditions on a class of differential equations that model particle dynamics which are influenced by the average statistic of the whole system. As such, these processes achieve mean-field limits when the number of particles increase asymptotically, whereby the iterated limits over time vs the number of units are commutative. In a specific case, we show that the mean-field limit of the system consists of mutually independent α-Wiener bridges, instead of Ornstein–Uhlenbeck processes typically seen in the classical setting. We provide examples with simulations for demonstration.