  Renormalization schemes and cutoff schemes allow for the introduction of
various distinct renormalization scales for distinct couplings. We consider the
coupled renormalization group flow of several marginal couplings which depend
on just as many renormalization scales. The usual $\beta$ functions describing
the flow with respect to a common global scale are assumed to be given. Within
this framework one can always construct a metric and a potential in the space
of couplings such that the $\beta$ functions can be expressed as gradients of
the potential. Moreover the potential itself can be derived explicitly from a
prepotential which, in turn, determines the metric. Some examples of
renormalization group flows are considered, and the metric and the potential
are compared to expressions obtained elsewhere.
