I would suggest that you don't try to put all of these solutions into action at one time, because if you do, when to problem subsides you'll never really know "exactly" where the problem was coming from and which solution worked to fix it. Start with one solution and see what results you get, and if that one doesn't work, try another one, and so on, until the problem is resolved. Now, in order for all forms of algae to grow, they require only two things; light and nutrients.

Lighting: The use of improper bulbs, lack of maintenance, and extended lighting hours are contributors that can lead to all sorts of algae problems.
Solutions: Only use bulbs that are designed for aquarium use, paying close attention to their spectral output; don't bombard the tank with an over abundance of light, follow the basic wattage rule of thumb; run the lights 8 to 9 hours a day.

Nutrients: Diatoms are most responsive to silca/silicates, but DOCs (Dissolved Organic Compounds), nitrates, and phosphates are food sources as well.
Silicates are most often introduced into aquariums by means of using unfiltered fresh tap water, the wrong kind of sand or substrate material, and through sea salt mixes that contain a higher than normal concentration of this element.
Solutions: Use RO/DI filtered make-up water, an aragonite type sand or substrate source, and a high quality sea salt mix.
Phosphates (PO4) are commonly introduced into aquariums by means of using unfiltered fresh tap water, and through many aquarium products that may contain higher than normal concentrations of this element, such as sea salt mixes, activated carbon, KH buffers, foods, and many other sources. Also, for established reef tanks the long-term use of Kalkwasser precipitates phosphates out of the water, and these phosphate based compounds can settle on and in the live rock and substrate.
Solutions: Use RO/DI filtered make-up water, a high quality sea salt mix, and be aware of the elements contained in other common aquarium products you may be using.