Probably mildew. A very helpful begonia expert who used to post here recommended spraying very lightly with Lysol. Also helps to increase air circulation, perhaps with a small fan. Some people use baking soda, but I don't remember the concentration--I just keep the Lysol spray can handy. I think it scares 'em--haven't had a problem since I started keeping it on a stand by my lights.

I heard begonias can develop powdery mildew. You could search for powdery mildew and see what remedies are recommended for this. I never heard about using Lysol but I'll have to look into this (interesting)!

the lysol is very effective, as is an occasional dusting/spraying of sulfur (stinky). you'll have to get the aerosol can, though.

-ming

Should I dilute the lysol? If so, at what rate?

as above, you should buy the lysol that comes in aerosol cans--which won't require diluting. just spray it straight.

-ming

I don't know if this information will be of any use to you or not, but several years ago I got mildew on my african violets every winter. My daughter gave me one of those small fountains suitable for a room. I run it constantly and haven't had mildew since. Why this worked I don't have a clue. Reason tells me more moisture in the room should produce more mildew, but its just the opposite.