Main panel: Mass in- and out-flux as a function of (z = 0) cloud mass. The former are shown in black, while the latter are in orange. Both rates correlate with cloud mass and are higher for more massive clouds. In the inset, we show the difference between the two rates: the net flux, i.e. in-flux minus out-flux. On average, clouds of all masses experience a net inflow of cold gas into them, with a higher net positive rate for more massive clouds.