We argue that the proton multiplicities measured in Roman pot detectors at an electron ion collider can be used to determine centrality classes in incoherent diffractive scattering. Incoherent diffraction probes the fluctuations in the interaction strengths of multi-parton Fock states in the nuclear wavefunctions. In particular, the saturation scale that characterizes this multi-parton dynamics is significantly larger in central events relative to minimum bias events. As an application, we study the centrality dependence of incoherent diffractive vector meson production. We identify an observable which is simultaneously very sensitive to centrality triggered parton fluctuations and insensitive to details of the model. Introduction Very high multiplicity events in protonproton (p+p) and proton/deuteron-nucleus (p/d+A) collisions at LHC and RHIC have revealed that the structure of such events is more complex and interesting than previously imagined [1][2][3][4]. In particular, interpreting the results of these experiments requires a deeper understanding of event-by-event multi-parton spatial fluctuations in protons and nuclei [5][6][7][8][9]. Incoherent diffraction in deeply inelastic scattering (DIS) of electrons off nuclei (e+A collisions) has been long understood as having the potential to provide insight into event-by-event fluctuations in the spatial structure of nuclei. A significant advantage of e+A collisions relative to p+A collisions is that the former is insensitive to the final state interactions that, in the latter, can complicate the extraction of the spatial parton structure of the proton and the nucleus.