luminescence of any light emitting device depends on the radiative recombination which in turn more dependent on the type of semiconductor used. If you talk about semiconductor lasers then it depends on the doping levels causing the degeneracy of the fermi level and population inversion. Indeed, the luminous power and current   is dependent on the supply voltage where it shows conventional diode-like characteristics. As the voltage is increased the radiative recombination rate is also increased thus intensity also. The following simulation results may give you better  explanation.

http://www.silvaco.com/examples/tcad/section38/example6/

The radiant (luminous) flux emission of semiconductor light-emitting diodes depends on the current flowing through them, not the voltage across their terminals. They exhibit high resistance and very little light emission until the voltage reaches two to three volts (depending on the device chemistry), then exhibit very low resistance as their light emission depends on the current (assuming a constant LED junction temperature). As such, they are often referred to as "constant-current" devices.

See Wikipedia or any number of "how-it-works" Web site articles for a more detailed description.

If voltage is increased then input power will increase. This will cause more radiative transition to take place and hence more photons will come out that will ultimately increase the optical output power and hence the luminosity of LED.

Yes it does, but indirectly. It is more correct to say that it depends on the current flowing through the LED since the radiative recombination is directly proportional to the number of carriers injected into p-n junction or the forward current density.

Thanks to all for valuable information