By mapping a set of input images to points in a low-dimensional manifold or subspace, it is possible to efficiently account for a small number of degrees of freedom. For example, images of a person walking can be mapped to a one-dimensional manifold that measures the phase of the person's gait. However, when the object is moving around the frame and being occluded by other objects, standard manifold modeling techniques (e.g., principal components analysis, factor analysis, locally linear embedding) try to account for global motion and occlusion. We show how factor analysis can be incorporated into a generative model of layered, 2.5-dimensional vision, to jointly locate objects, resolve occlusion ambiguities, and learn models of the appearance manifolds of objects. We demonstrate the algorithm on a video consisting of four occluding objects, two of which are people who are walking, and occlude each other for most of the duration of the video. Whereas standard manifold modeling techniques fail to extract information about the gaits, the layered model successfully extracts a periodic representation of the gait of each person.