The most common analysis pipeline in applied topology involves computing persistent homology of some filtered simplicial complex derived from data, then using the resulting persistence diagram as a feature for statistical or ML techniques. This is the default in part because it is very difficult to compare persistence modules computed from different data sets directly. In an ideal world, we would try to approximate a function between the systems underlying data sets and apply functoriality to build induced maps. However, in many applications it is unreasonable to assume the existence of such functions. Even if we have full control over and knowledge of the state of one of the systems, hidden variables and noise in the other will usually result in a range of resulting behaviors and states in the other. Thus, the best we can hope for is to observe a relation between system states, in the guise of correlation or other cross-similarity. In this talk, we describe a method for leveraging such observations to compare persistent homology classes between related persistence diagrams. This is joint work with Iris Yoon and Robert Ghrist.