+1 on the adding chemicals, but adding a pouch of PhosGuard or Chemi-Pure Elite to your filter can only help, not hurt. Definitely do not go with a chemical algaecide.
Many many years ago, I had a terrible diatom outbreak when I put two blue gouramis into a 12 gallon Eclipse system (my first tank). The standard CFL light on the Eclipse seemed off to me, very yellowish in its color rendering. No live plants.
I used Algone (
www.algone.com) and it did get rid of the problem, but it's expensive for what it is (and they don't say what it is...) but it didn't hurt the apple snail I had in there (oy...first tank shame...) so I don't believe it is an algaecide. So you could try that if you're so inclined.
Right now I am having a diatom outbreak on my 55 gallon goldfish tank:
http://www.aquariacentral.com/forums/showthread.php?t=217663
Do you have fast growing plants in your tank? I am using hornwort and floating anacharis, along with Amazon frogbit and duckweed - which has a hard time keeping up with the appetites of the two black moors in there. As the plants really start thriving (the hornwort is taking off, it loves a coldwater tank) the diatoms start to look less vigorous. Right now I am at the point where they are looking very opaque if that makes sense...very deep in color. They almost seem like they are starting to turn up at the edges, so I take it that *something* is happening.
I've done one 90% water change (didn't stress the fish at all, but I have well water with no chlorine in it...) and that seemed to help a lot. I will probaly do another in a couple of weeks, my nitrates are already at 20 ppm again. Goldfish are messy!
Eventually, I think the excess silicates will be used up. My theory is they are coming from my pool filter sand...which I didn't rinse since it's very "clean" sand. I've always used sand, but never pool filter sand - always (rinsed and rerinsed) "leveling sand" from Lowe's. The difference in texture and color is noticeable.
This 55 also has double as much light as my other 55, which has always been spotlessly clean...
So that's my theory...my other planted tanks (two 10 gallon tanks) have never had this problem. I hope you figure out what your root cause is, it may well have to do with lighting - try asking in the Planted Aquarium section for tips on your bulbs!