Take a look at this simplistic view:
We are operating right down at the ~ 2V region where curves converge, tend to be more horizontal and all bets are off. The dotted line at 20 mA is where they start coming on-song, predictably.
Edit Ours are being run at less than 1/100th of that level.
If you had real data on these specific diodes, from a specific batch, and plotted on a log scale, I think (surmise) that they would be operating in a very non-linear (and undocumented) region at these current densities, depending on the area of the junction, indirectly related to size of the die. They donāt behave much differently from a basic PN diode, just the āswitching regionā between conduction and not, is raised in voltage (e.g about 0.6v for plain silicon) Leds have a different band-gap, depending on frequency (colour) of light emitted.
And they are made of compound semiconductors, not silicon (Gallium, Indium, with Arsenic doping to name a few), applied epitaxially on top of plain silicon, or silicon carbide (Cree) which may or may not be ideally constructed, depending on skills of the manufacturer. Making blue LEDs was thought impossible, until a very clever Japanese fellow showed how to do it, and then UV. Red, amber, green, dead easy by comparison. Now we have all sorts of colours. White ones donāt exist, they are typically mainly a UV emitter with precisely tuned phosphor mix on top that converts UV to the high CRI white light we love. Making the phosphors is a closely guarded secret, making them last and be stable for thousands of hours even more so.
Itās dead clever.
Anyway, bottom line is that itās tricky to run even tiny LEDs at very low currents consistently well. Thorfire got caught out when they changed between prototypes (working well) and what might have seemed like an identical alternative, according to datasheet, but now we know differently.