Why does the rate of change of potential difference between two capacitor plates decrease as the capacitor discharges?

Current, I, is related to voltage by Ohm's law, I=V/R. As the capacitor discharges, the current will decrease as less charge is "released" from the capacitor. From Ohm's law, we would expect lower currents to result in lower potential differences (assuming a constant resistance), thus as the current decreases, the potential difference also decreases, at an exponential rate.