Why does algae seem to have the ability to spontaneously generate?

I understand how algae grows and whatnot but what I cant seem to understand is where in the hell it comes from. If i get a fish tank and fill it up with RODI water and put no fish or any other organic matter in there and just leave it for a week somehow that tank will still have algae growing in it. Where the hell did it come from?

All I can really think is that algae spores are present in all water waiting for the right conditions to grow but at the same time this is RODI water im talking about. Shouldnt any of said spores been eliminated by this process? Ive even gone as far as putting RODI water through a UV sterilizer first and still algae grows. Are algae spores just extremely resilient or something?