Using video microscopy and simulations, we study the diffusion of probe particles in a wide range of complex backgrounds, both crystalline and disordered, in quasi-2D colloidal systems. The dimensionless diffusion coefficients D^{*} from different systems collapse to a single master curve when plotted as a function of the structural entropy of the backgrounds, confirming the universal relation between diffusion dynamics and the structure of the medium. A new scaling equation is proposed with consideration for the viscous friction from the solvent, which is absent in previous theoretical models. This new universal law quantitatively predicts the diffusion coefficients from different systems over several orders of magnitude of D^{*}, with a single common fitting parameter.