We have developed a dust emission model in order to reproduce the evolution of the far-infrared (FIR) to sub-millimetre (sub-mm) dust emission properties which is observed in the transition between the diffuse and the dense interstellar medium (ISM). We propose that the coagulation of grains into fluffy aggregates could be the process responsible for the observed dust evolution from the diffuse to the dense ISM in the Galaxy. In dense clouds, dust coagulation can explain the increase in grain size, the decrease in the grain temperature in excess of that predicted by extinction, the sub-mm emissivity excess and the decrease in the small grain abundance.