most basic laser diode driver?
If you have a regulated power supply, a simple resistor will do to take the laser above its threshold point. More complexity can involve a thermistor to lower resistance as temperature rises keeping the laser current at a slightly higher value at higher temperatures. Here is a typical laser characteristic for a device supplied by Hamamatsu: -



A more complex circuit would be needed if the laser were to be used as a datacomms device but this would involve only one extra inductor and a capacitor.

Going further, to higher powers and several manufacturers make chips that monitor the inbuilt photodiode inside a lot of lasers. They do this to protect the device from excessive currents.

Using an LM317 current limiting supply seems reasonable to me but the devil is in the detail and a circuit would be needed to be looked at for greater confidence (plus the data sheet of the laser).