  In 1988, Haagerup and St{\o}rmer conjectured that any pointwise inner
automorphism of a type $\rm III_1$ factor is a composition of an inner and a
modular automorphism. We study this conjecture and prove that any type $\rm
III_1$ factor with trivial bicentralizer indeed satisfies this condition. In
particular, this shows that Haagerup and St{\o}rmer's conjecture holds in full
generality if Connes' bicentralizer problem has an affirmative answer. Our
proof is based on Popa's intertwining theory and Marrakchi's recent work on
relative bicentralizers.
