A central problem in historical linguistics is the identification of historically related cognate words. We present a generative phylogenetic model for automatically inducing cognate group structure from unaligned word lists. Our model represents the process of transformation and transmission from ancestor word to daughter word, as well as the alignment between the words lists of the observed languages. We also present a novel method for simplifying complex weighted automata created during inference to counteract the otherwise exponential growth of message sizes. .