We use simple analytical models of the buildup of the dust component and compare these with radial dust distributions derived from observations of SINGS galaxies. The observations show that dust gradients are indeed typically steeper than the corresponding metallicity gradients and our models indicate very little dust destruction, but significant dust growth in the interstellar medium for most of these galaxies. Hence, we conclude that there is evidence for significant non-stellar dust production, and little evidence for dust destruction due to supernova (SN) shock waves. We find that dust is reprocessed rather than destroyed by shocks from SNe. Finally, we argue that dust abundances derived using standard methods may be overestimated, since even very ‘generous’ estimates of the metallicity result in dust-to-metals ratios above unity in several cases, if the dust abundances given in the literature are taken at face value.