Finding required maximum current rating for a diode which will run in PWM mode
Can we always assume that \$I_{FM} = D \times I_{ON}\$ for all duty
  cycle rates and PWM frequencies?


No, that would be naive. Assume duty cycle is virtually one, you wouldn't choose a diode with a continuous forward current maximum close to the working current. That would be asking for trouble - you need to de-rate appropriately, probably to about two-thirds (off-the-cuff rule of thumb). Diodes tend to be high failure devices, especially in power rectification and if you were familiar with MIL-HDBK-217F\$^1\$ you'd probably derate more to give a useful life from the device.

If the duty cycle were low then you will get to a point where you can reasonably rely on the peak current handling ability of the diode.



\$^1\$ this document is still very useful despite its age and predicts the reliability of components based on application and ratings.