This work demonstrates that quantum diffractive collisions are governed by a universal law characterized by a single parameter that can be determined experimentally. Specifically, we report a quantitative form of the universal, cumulative energy distribution transferred to initially stationary sensor particles by quantum diffractive collisions. The characteristic energy scale corresponds to the localization length associated with the collision-induced quantum measurement, and the shape of the universal function is determined only by the analytic form of the interaction potential at long...