Generating realistic human motion is an important task in many computer vision and graphics applications. The rich diversity of human body shapes and sizes significantly influences how people move. However, existing motion models typically ignore these differences and use a normalized, average body size. This leads to a homogenization of motion across human bodies that limits diversity and that may not align with their physical attributes. We propose a novel approach to learn a generative motion model conditioned on body shape. We demonstrate that it is possible to learn such a model from unpaired training data using cycle consistency and intuitive physics and stability constraints that model the correlation between identity and movement. The resulting model produces diverse, physically plausible, dynamically stable human motions that are quantitatively and qualitatively more realistic than the existing state of the art.