No Coraline will not "flow with the current". If I understand you correctly, and I think I do, you have a diatom bloom, which, on a new tank could signal the end of the cycle, or that the end is near.
The purple algae is not really algae. It is cyno-bacteria. Do a google search on it. Or search this bb. Three major things cause cyno ["Red Slime algae"]
1. Dissovled organics. Are you running a skimmer?
2. Wrong Spectrum or old lighting. What do you have for lights now?
3. Poor water quality. What do you use for water? RO/DI or Tap. Tap water will have phosphates, silicates and nitrates, basic food for cyno.
You can use, and people will tell you to, cemicals such as Poly-Ox by Kent to rid this pest. But it is just a band-aid. Fix the source, and you will have no problems from this.
The diatoms are normal to a new tank. Might want to look into getting a clean up crew that will take car of the BROWN diatoms.
You are correct on the Coraline Algae. It is a hard crusty substance that will come with age and proper water quality, additives, lighting ect, to your tank.