First, here are the definitions I am working with: Given an undirected graph $G = (V,E)$ and vertices $s, t \in V$ we wish to either find the number of vertex disjoint paths from $s$ to $t$ or to find the number of edge disjoint paths from $s$ to $t$.
I am trying to show the instance of one problem can be transformed to an equivalent instance of the other. I was able to show one direction: in particular, given an instance of the edge disjoint path problem, I can convert it to an equivalent instance of the vertex disjoint path problem by using the line graph $L(G)$. The only thing that I am not sure about is what to make of $s$ and $t$ as they are no longer defined in $L(G)$.
However, for the other direction, I have no idea how to transform an instance of the vertex disjoint problem to an equivalent instance of the edge disjoint problem.
The reduction need not be one-to-one (i.e if there are $k$ paths in the vertex-disjoint case, there could be $k'$ paths in the edge disjoint case... as long as we can show how to go from $k'$ to $k$.