  The nonlocal bosonic theory obtained from integrating out all anticommuting
and auxiliary variables in a globally supersymmetric theory is characterized by
the Nicolai map. The latter is generated by a coupling flow functional
differential operator, which can be canonically constructed when the
supersymmetry is realized off-shell. Given any scalar superfield theory, we
present a universal formula for both the Nicolai map and its inverse in terms
of an ordered exponential of the integrated coupling flow operator. We
demonstrate that our formula also holds for supersymmetric gauge theories.
