Joint alignment of a collection of functions is the process of independently transforming the func- tions so that they appear more similar to each other. Typically, such unsupervised alignment al- gorithms fail when presented with complex data sets arising from multiple modalities or make re- strictive assumptions about the form of the func- tions or transformations, limiting their general- ity. We present a transformed Bayesian infinite mixture model that can simultaneously align and cluster a data set. Our model and associated learning scheme offer two key advantages: the optimal number of clusters is determined in a data-driven fashion through the use of a Dirichlet process prior, and it can accommodate any trans- formation function parameterized by a continu- ous parameter vector. As a result, it is applica- ble to a wide range of data types, and transfor- mation functions. We present positive results on synthetic two-dimensional data, on a set of one- dimensional curves, and on various image data sets, showing large improvements over previous work. We discuss several variations of the model and conclude with directions for future work.