Will White Marks from an IPL Burn Heal on Its Own?

Loss of skin pigment after a burn may be permanent. 1 month is too soon to tell. If it is a "discoloration" as your dermatologist described, it likely will improve over the ensuing months. You should have your doctor follow you closely, or consider getting a second opinion from a reputable cosmetic dermatologist familliar with IPL and laser treatments.

Though it is still too soon to tell completely, generally speaking if the pigment has disappeared from an area due to damage or trauma it can be permanent. (Because the cells that produce the pigment have either been permanently damaged or just 'stunned' temporarily)  After only a month there is still a good chance that the skin will regain its color but we can't be certain.  Definitely protect the new skin from the sun with a good sunscreen or sunblock....do NOT try to tan the area to match the other skin.  This will not work and may only aggravate the problem.  Make sure to follow up with the Dermatologist and NP who did your treatment so they can advise you.