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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 quantitative formula is proposed with considerations for the viscous frictions from the solvent,which is absent in previous theoretical models that fail to fit to the experimental data.This new universal law quantitatively predicts the diffusion coefficients from different systems over several orders of magentudes of D*,with a single fitting parameter.Our findings not only provide a deep understanding of the universal diffusion-structure relation but also constitute a solid experimental verification.