The objective of dimensionality reduction algorithms is to discover "simpler" descriptions of complicated, high-dimensional data.  The hope is that such dimension-reduction mappings might simplify task performance (e.g. classification), provide efficient data representation, or spur creative interpretations of the data.  By combining two classic techniques with rich geometric structure - Wasserstein distances and Isomap - we are exploring a new nonlinear dimensionality reduction technique with interesting properties.  Computational experiments will be shown to illustrate the technique for image data.