I would look into this further, as it may not be diatoms but more serious.
"Brown algae" can refer to more than just diatoms as some red algae can be brown, dark green, or black in colour. And I think from the best I can see in the photos, what you are calling brown may not be diatoms.
Daitoms will very easily rub off using your fingertip, from plant leaves for example. Brush algae (which is a red algae that has more than one form and can be dark brown, black, dark grayish-green or reddish-brown) will not rub off. This is the easiest way to tell the difference.
Another thing is the presence of the green algae on the rock, which would tend to discount diatoms as bee more likely to indicate brush algae, as these are due to an imbalance of light/nutrients and most usually an excess of light (too bright, or too long in duration).