If the converter runs in continuous mode, the formula applies for the output voltage. The converter enters continuous mode when its output current is large enough that the inductor current "touches" zero just before the switch turns on again. If the output current now increases, the inductor DC current increases, but AC (pp) current stays the same, determined by the switch duty cycle. The inductor doesn't get fully discharged anymore, and thus the output voltage doesn't rise.
As long as the converter runs in discontinous mode (inductor current reaches zero before the switch turns on again), it fully discharges into the capacitor and causes the voltage to rise. Think of some minimum energy quanta that must be transferred each cycle. As soon as continuous mode is reached, more than the minimum quanta is transferred per cycle, implicit determined by the output current. The minimum quanta is determined by inductor value and its AC (p-p) current, not the DC current.