We have developed Simulation-based Reconstructed Diffusion (SbRD) to determine diffusion coefficients corrected for confinement effects and for the bias introduced by two-dimensional models describing a three-dimensional motion. We validate the method on simulated diffusion data in three-dimensional cell-shaped compartments. We use SbRD, combined with a new cell detection method, to determine the diffusion coefficients of a set of native proteins in Escherichia coli. We observe slower diffusion at the cell poles than in the nucleoid region of exponentially growing cells, which is independent of the presence of polysomes. Furthermore, we show that the newly formed pole of dividing cells exhibits a faster diffusion than the old one. We hypothesize that the observed slowdown at the cell poles is caused by the accumulation of aggregated or damaged proteins, and that the effect is asymmetric due to cell aging.