I have a small original canon Demi, that has a bunch of tiny scratches on the front. If you shine a light thru it you'll basically see a big mesh of tiny scratches, in the pictures it gives a soft diffused look in a circle in the middle of the pictures.
One method I heard of repairing was using jeweler's polish which is a very fine abbrassive and polishing the front of the lens, but you had to be careful.
The other one that I'm curious about was those eyeglass repair kits that you can remove scratches from glasses. Supposibly they can make glasses that look like they were rubed down with steel wool look new again. I'm wondering if I got one of those repair kids cheap if I could get rid of the diffusion in the center of the little lens on my Canon Demi. Or at least know if its possible to remove the material once applied (in case the tests dont fair well). My assumption is that it may work, but that it may affect a camera lens, more than it does eyeglases as some may say eye glasses don't need to be as critical about minor surface curvature.
Also here are some pictures from the last time I went out shooting with the demi if you are curious.
Its either that or leave the demi at home, til I need some soft diffused shots. But I just kinda liked the idea of having a little half frame snapshooter around provided I could get the shots to appear normal, if not least sharp enough for a 4x6.