Yep, the diodes keep the caps from unfilling back to the source so the caps supply current to the rest of the system when the input voltage is lower than the current cap voltage, only when the input voltage is greater than the cap voltage by the diode voltage drop do they fill back up. But they fill at the rate set by the capacitor’s impedance the transformer’s impedance, the power cord’s, the outlet’s, etc.
You can see that part pretty clearly with a simpler (but less efficient) circuit:
