Given a collection of surfaces with common key features, that have a rough correspondence, we consider the shape variation in the geometric configuration. However, this is often challenged due to the subtle variation of these shapes. In our study, we view these shapes as lying on a manifold, where each sample point is a manifold in its own right. The dataset is then a collection of other low-dimensional manifolds with common key features, that are in rough correspondence; in many cases, this can be reasonably modeled as a (nonlinear) fibre bundle with a connection. We use this connection to study the base manifold geometry using fibre bundle diffusion.