This is a charge pump. It works by literally pumping charge like a water pump would pump water. Those capacitors will not have an RC discharge characteristic because there are no 'R's in the circuit.
Use this as a thought experiment to understand what's going on:
Imagine the capacitors are flexible membranes, and the diodes are 1-way valves (ignore Vf for now). That should make it clear why the circuit behaves the way it does.
Edit: Ok, here. This simulation has all of the voltages and currents, and simplifies things by using a square wave instead of a sine wave. You need to pay attention to the current in the circuit to understand what is going on.
simulate this circuit – Schematic created using CircuitLab
This circuit will behave in a more complex way if there is a load resistor across C2, because in this case, after the first cycle, C2 becomes completely charged and nothing else happens.