Diadems can be worn when a head of state brings a full State Visit to the Holy See. I doubt we will see full protocol with diadems et al during the pontificate of Pope Franciscus.
During a State Visit, the Pope himself dresses up too, wearing a choir dress over his usual white soutane, a silk mozzetta (red during the year, white during Easter and Christmas time, trimmed with fur when it is cold). In contrary to his predecessors Pope Benedictus XVI and Pope Johannes Paulus II, the present Pope has never followed this protocol so far, which means that (royal) visitors themselves can "lower down" as well. After all, when the Pope wears his "daily suit" then also the royals can wear their "daily suit" if wanted.
Pope John Paul II, Pope Benedictus XVI and Pope Paulus VI dressed up to highest state protocol, being a par to receive heads of state dressed completely up: