Vertex-disjoint paths and edge-disjoint branchings in directed graphs

A theorem of J. Edmonds states that a directed graph has k edge-disjoint branchings rooted at a vertex r if and only if every vertex has k edge-disjoint paths to r. We conjecture an extension of this theorem to vertex-disjoint paths and give a constructive proof of the conjecture in the case k = 2.