Yup! Diatoms. The scourge of new aquarists. Mine almost drove me crazy. As hard as this will seem...just wait 'em out. I thought about peroxide and other such...got some good advice on here to not do anything stupid. Eventually, long after they've destroyed your confidence and desire to continue in the hobby, they will go away. Mine lasted for 6-8 weeks (bit longer than most). Make sure you keep some NO3 and PO4 (you are already it seems). Blacking out tank helped....temporarily. They came back. I did lose some zoas and birdsnest during my outbreak. Don't add any more corals until it's over.
One day I woke up and they were just "less". Next day better...and so on.