ABSTRACT The dust mass absorption coefficient, κd is the conversion function used to infer physical dust masses from observations of dust emission. However, it is notoriously poorly constrained, and it is highly uncertain how it varies, either between or within galaxies. Here we present the results of a proof-of-concept study, using the DustPedia data for two nearby face-on spiral galaxies M 74 (NGC 628) and M 83 (NGC 5236), to create the first ever maps of κd in galaxies. We determine κd using an empirical method that exploits the fact that the dust-to-metals ratio of the interstellar medium is constrained by direct measurements of the depletion of gas-phase metals. We apply this method pixel-by-pixel within M 74 and M 83, to create maps of κd. We also demonstrate a novel method of producing metallicity maps for galaxies with irregularly sampled measurements, using the machine learning technique of Gaussian process regression. We find strong evidence for significant variation in κd. We find values of κd at 500 $μ$m spanning the range 0.11–0.25 ${\rm m^{2}\, kg^{-1}}$ in M 74, and 0.15–0.80 ${\rm m^{2}\, kg^{-1}}$ in M 83. Surprisingly, we find that κd shows a distinct inverse correlation with the local density of the interstellar medium. This inverse correlation is the opposite of what is predicted by standard dust models. However, we find this relationship to be robust against a large range of changes to our method – only the adoption of unphysical or highly unusual assumptions would be able to suppress it.