ESD / TVS / Over-voltage diode selection - leakage current into power supply
The leakage current of diodes produces a constant current flow. It's defined for conditions where the diode is not actually in conducting state. Thus, these diodes rise your total power consumption like a parallel resistor.
Normally this current is very low, we are talking about \$nA\$ or \$\mu A\$.
However, this values depends on your type of diode and e.g. the clamping voltage of TVS diodes. In generally, it's defined in the datasheet.