I suspect what you are seeing is the natural maturation of the sunflower. Small bugs are attracted to the center of the sunflower as that's where the mectar and pollen is. When sunflower blooms, in a few days the petals whither the heads bow and the leaves start to yellow and the seeds ripen.
That's just what they do.
Linda C

Oh, Linda

Thank you, but I do not think they were maturing because it became really black, not brown. And why do they twist and get deformed...? Is it normal?
I showered them with water, and now the flies are gone.

I think I have the same problem. This is my first time planting sunflowers & I have watched them daily. Mine are the 'giant'variety & the stems are green & thick. One huge flower looks as though it was trying to split in half so it looks deformed to me. I have bright yellow petals & seeds were forming & then the heads bent over & there is a blackish smear in the center of the heads. I don't think they ever seeded since I never saw birds but I never had black bugs. I've read thru sunflower diseases but nothing describes this. I must admit, I don't know what heathy, natural sunflower seed looks like either. I have not lost petals so I don't think this is maturation either & the leaves are healthy. The back of the heads are still green. My flowers are in Maryland