  We develop Korevaar-Schoen's theory of directional energies for metric-valued
Sobolev maps in the case of ${\sf RCD}$ source spaces; to do so we crucially
rely on Ambrosio's concept of Regular Lagrangian Flow.
  Our review of Korevaar-Schoen's spaces brings new (even in the smooth
category) insights on some aspects of the theory, in particular concerning the
notion of `differential of a map along a vector field' and about the
parallelogram identity for ${\sf CAT}(0)$ targets. To achieve these, one of the
ingredients we use is a new (even in the Euclidean setting) stability result
for Regular Lagrangian Flows.
