The aim of this work is to learn generative models of object deformations in an unsupervised manner. Initially, we introduce an Expectation Maximization approach to estimate ma linear basis for deformations by maximizing the likelihood of the training set under an Active Appearance Model (AAM). This approach is shown to successfully capture the global shape variations of objects like faces, cars and hands. However the AAM representation cannot deal with articulated objects, like cows and horses. We therefore extend our approach to a representation that allows for multiple parts with the relationships between them modeled by a Markov Random Field (MRF). Finally, we propose an algorithm for efficiently performing inference on part-based MRF object models by speeding up the estimation of observation potentials. We use manually collected landmarks to compare the alternative models and quantify learning performance.