We present an information-theoretic approach for integration of multi-resolution data into multiscale simulations. This general framework is used to up- and down-scale equations of fluid flow in heterogeneous porous media. Fine-scale information can comprise observational data and/or simulation results related to both system states and system parameters. It is aggregated into its coarse-scale representation by setting a probabilistic equivalence between the two scales, with parameters that are determined via minimization of observables error and mutual information across scales. The same quantities facilitate the use of coarse-scale data to constrain compatible fine-scale distributions.