Laser diodes only work over a restricted range of currents, too little and they behave rather like ordinary LEDs, too much and they instantly burn out. The laser diodes you show only have two wires so the regulator circuit is built in to them but you still have to provide a constant voltage. More accurate lasers have at least three wires and the third is to allow the light output to be monitored so the control circuit can maintain constant brightness.
Trying to adjust the brightness with that PWM controller almost certainly wont work, it uses variable length pulses at full voltage (minimum is 6V) to give the appearance of dimming in an incandescent lamp. The LED needs a regulated 2.2V and may not like being pulsed at all.
What are you trying to achieve?
Brian.