  We establish a general superposition principle for curves of measures solving
a continuity equation on metric spaces without any smooth structure nor
underlying measure, representing them as marginals of measures concentrated on
the solutions of the associated ODE defined by some algebra of observables. We
relate this result with decomposition of acyclic normal currents in metric
spaces.
  As an application, a slightly extended version of a probabilistic
representation for absolutely continuous curves in Kantorovich-Wasserstein
spaces, originally due to S. Lisini, is provided in the metric framework. This
gives a hierarchy of implications between superposition principles for curves
of measures and for metric currents.
