Thanks for your question.
I believe the plant is a rhododendron and this non-research site has pictures that look like yours: Help! Azaleas and Rhododendrons dying from white fungus! (houzz.com)

So, the white growth could be downy or powdery mildew 
More on Mildew (rhododendron.org)
At this point you should prune the affected branches so there's more circulation. Don't over water to limit humidity.  Also remove any leaf debris on the ground that could harbor the mold spores.

You could treat with sulfur-based fungicides or neem oil. If you do use chemicals, you must follow the directions exactly.  Neem oil is a natural fungicide and I'd try that first.  This site suggests using baking soda, another natural item: How to Get Rid of Fungus on Rhododendron Plant (livetoplant.com)

To be thorough I should mention that I saw some articles indicating that the white growth could also be a type of scale.  I am including the link White fungus or pest on our rhododendron/azaleas - Ask Extension

However, without a test to determine the source, I'd tend toward the mildew diagnosis.  I hope this helps you cope with this mildew fungus.