This is a half-wave parallel voltage multiplier. Contains several charge-pump stages. Each cycle a current spike travels through the capacitors. This might explain the solid red area in your graph (because cycles are numerous and close together).
Or else the led is the type of load which gobbles it's own spike of current per cycle. A diode is itself a voltage regulator. It's quick-acting.
It helps that you installed resistance at one or two places in the circuit. However this does not reduce all the spikes through the circuit. In addition try putting a low-ohm resistor inline with each capacitor. Then the charging and discharging waveforms are easier to observe.
I could be wrong. Often a solid area on a graph is created by parasitic oscillations (the kind which might occur in self-resonating components as suggested by post #2). Normally your circuit is not the kind that should produce oscillations. Since your frequency is in the Ghz range, then try lengthening the time axis, so it creates some white space between waveforms in the solid red area.