I use the Atlas of QGIS 3.2. I already figured out how to show only attributes inside current Atlas feature using $id = @atlas_featureid.
My problem is, as a coverage layer I am using layer with municipality borders, although my featured layer has borders of smaller administrative units. When I use the $id = @atlas_featureid, Atlas only shows one diagram per Map.
I partially found a solution to hide diagrams outside current map feature in this thread, but it doesn't solve my problem.