How do I apply Map[] to a function using two arguments in Mathematica?

In general, I was trying to compute the norm of the difference between every set two elements in a list which looks something like

X = {{1,2,3,4,5},{6,7,8,9,10},{11,12,13,14,15}}

therefore evaluating

Norm[X[[1]]-X[[2]]]
Norm[X[[1]]-X[[3]]]
Norm[X[[2]]-X[[3]]]

Now, applying Outer[] is one possible way how to do this

Outer[Norm[X[[#1]] - X[[#2]]] &, {1,2,3}, {1,2,3}]

but unfortunately it results in a quite slow code if I increase the number of elements in X and the length of each element.

Is there any possible way to construct a Map[] operation? Something like

MapThread[Norm[X[[#1]] - X[[#2]]] &,{{1,2,3},{1,2,3}}]

does not work give the desired "currying" which I was looking for. I'm using Mathematica Version 11.2.0.0, so I don't have access to Curry[].

Would be happy about any advice!

Solution

mX = {{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}, {11, 12, 13, 14, 15}}
Apply[Norm@*Subtract, #] & /@ Subsets[mX, {2}]

Two equivalent approaches:

(Norm@*Subtract) @@@ Subsets[mX, {2}]
Apply[Norm@*Subtract, Subsets[mX, {2}], {1}]