We present a probabilistic model of diachronic phonology in which individual word forms undergo stochastic edits along the branches of a phylogenetic tree. Our approach allows us to achieve three goals with a single unified model: (1) reconstruction of both ancient and modern word forms, (2) discovery of general phonological changes, and (3) selection among different phylogenies. We learn our model using a Monte Carlo EM algorithm and present quantitative results validating the model.