Distilled water, sold by the gallon at grocery stores usually, would work for this as well.
There are two key nutrients that will favor diatom growth in a tank.. silicates and iron. Iron will cause a rip-roaring outbreak of diatoms, especially in a ten gallon, practically over night. If you are dosing iron for the macros due to anecdoctal suggestions here on RC, cut back your dosage in half until you stop seeing the diatoms appear.
If you're not dosing anything but the usual reef stuff, then you likely just have nutrient high tap water that the purifier isnt entirely removing. Try to do some water changes ASW made up with distilled and see how that helps out.
I thought I might mention why silicates in particular are usually the culprit in tap water that charge a diatom outbreak. Diatoms - of which there are several thousand species - have an outer shell or capsule that is made up almost entirely of a few organic molecules and a framework of silicon that is engineered by the little algae cells to protect it from the environment. If you dont have any or very little silicates in the water, they have nothing to grow on. Lots of silicate means they can make lots of silica-based shells so you get the population explosion.
Iron just happens to be a favorite nutrient of diatoms in the world's oceans.. they seem to be the leading uptake route for iron in the sea by phytoplankton.
Good luck!
>Sarah