Understanding the role of diffusion in catalysis is essential in the design of highly active, selective, and stable industrial heterogeneous catalysts. By using a combination of advanced in situ spectroscopic characterization tools, particularly quasi-elastic and inelastic neutron scattering, we outline the crucial differences in diffusion modes and molecular interactions of active sites within solid-acid catalysts. This, coupled with 2D solid-state NMR and probe-based FTIR spectroscopy, reveals the nature of the active site in our SAPO-37 catalyst and affords detailed information on the evolution of solid-acid catalysts that can operate at temperatures as low as 130 °C, for the Beckmann rearrangement of cyclohexanone oxime to ε-caprolactam (precursor for Nylon-6). The versatility of this approach leads to structure−property correlations that contrast the dynamics of the diffusion process in the different materials studied. Our results illustrate the power of these techniques in unravelling the interplay between active site and molecular diffusion in single-site heterogeneous catalysts, which can play a vital role in designing low-temperature, sustainable catalytic processes.