A summary of the requirements for modulational (thick‐layer) diffusion to exist in a particle synchrotron is presented and applied to a simple tune‐modulated collider model of the Fermilab Tevatron where the only nonlinearities present are two beam‐beam kicks. For certain realistic tune modulation parameters and single‐particle base tunes, amplitude growth is observed over timescales appropriate to diffusive models. The character of this growth has qualitative features that are similar to those predicted by modulational diffusion models, but is significantly different in that the amplitude growth is exponential in time, not root‐time as in classical diffusion. Some possible explanations for this effect are briefly noted, and impact of the possible existence of such a mechanism on future Fermilab collider upgrades is mentioned.