Recent discoveries have highlighted the dramatic evolutionary transformation of massive, ground-dwelling theropod dinosaurs into light, volant birds. Here, we apply Bayesian approaches (originally developed for inferring geographic spread and rates of molecular evolution in viruses) in a different context: to infer size changes and rates of anatomical innovation (across up to 1549 skeletal characters) in fossils. These approaches identify two drivers underlying the dinosaur-bird transition. The theropod lineage directly ancestral to birds undergoes sustained miniaturization across 50 million years and at least 12 consecutive branches (internodes) and evolves skeletal adaptations four times faster than other dinosaurs. The distinct, prolonged phase of miniaturization along the bird stem would have facilitated the evolution of many novelties associated with small body size, such as reorientation of body mass, increased aerial ability, and paedomorphic skulls with reduced snouts but enlarged eyes and brains.