Relation between diodes and laser diodes
Bespoke Current-Voltage relationships do not provide explanations of how light emitting diodes work. It is characterization of the input / output relationship: not the lasing mechanism.

As an analogy: the relationship between my Toyota Camry's velocity (measurable output) and accelerator position (controllable input) does not explain the mechanism (Pressure-volume work) of why the vehicle moves forward.

Resistors are linear models of current produced when a voltage (battery) is applied.  In contrast: Diodes are NONLINEAR voltage-current devices.  This graph shows the output current as a function of the voltage across the diode (see bottom right of diagram).   



Said explanations and relationship only address voltage-current relationships and not luminosity (light emitting capability).  The voltage-current relationships are important (useful) in selecting resistors to limit reasonable currents through LEDs and not damage the LED.