  Fujino gave a proof in [Fuj03] for the semi-ampleness of the moduli part in
the canonical bundle formula in the case when the general fibers are K3
surfaces or Abelian varieties. We show a similar statement when the general
fibers are primitive symplectic varieties with mild singularities. This answers
a question of Fujino raised in the same article. Moreover, using the structure
theory of varieties with trivial first Chern class, we reduce the question of
semi-ampleness in the case of families of K-trivial varieties to a question
when the general fibers satisfy a slightly weaker Calabi-Yau condition.
