Human languages may be shaped not only by the (individual psychological) processes of language acquisition, but also by population-level processes arising from repeated language learning and use. One prevalent feature of natural languages is that they avoid unpredictable variation. The current work explores whether linguistic predictability might result from a process of iterated learning in simple diffusion chains of adults. An iterated artificial language learning methodology was used, in which participants were organised into diffusion chains: the first individual in each chain was exposed to an artificial language which exhibited unpredictability in plural marking, and subsequent learners were exposed to the language produced by the previous learner in their chain. Diffusion chains, but not isolate learners, were found to cumulatively increase predictability of plural marking by lexicalising the choice of plural marker. This suggests that such gradual, cumulative population-level processes offer a possible explanation for regularity in language. (Contains 2 figures.)