We present a probabilistic approach to language change in which word forms are represented by phoneme sequences that undergo stochastic edits along the branches of a phylogenetic tree. This framework combines the advantages of the classical comparative method with the robustness of corpus-based probabilistic models. We use this framework to explore the consequences of two different schemes for defining probabilistic models of phonological change, evaluating these schemes by reconstructing ancient word forms of Romance languages. The result is an efficient inference procedure for automatically inferring ancient word forms from modern languages, which can be generalized to support inferences about linguistic phylogenies.