I´m no semiconductor expert, but remember some stuff:
A diode in reverse polarity creates a so called depletion zone. This is free of charge carriers, until the breakdown voltage is reached.
In reverse breakdown, charge carriers pass through this zone with quite high energy. This seems to induce some kind of F-centers, in other words atoms that are ionized in the otherwise neutral volume.
So far I think it´s solid physics. Now it gets speculation: The F-centers may act as crystallographic defects around the junction. Crystallographic defects can transform a semiconductor to a resistor.
What´s really astonishing is that this effect seems to be reversible, but maybe the flow of current through the diode in forward direction neutralizes the defects again.
It´s just a theory - maybe it´s also just some artifact from the curve tracer.
Did you try this with other components? With normal diodes? Zener diodes? Other color LEDs?
In case it really is a resetable material property it would be an exotic form of 1-bit-memory