  We show that the non-perturbative dynamics of $\mathcal{N}=2$ super
Yang-Mills theories in a self-dual $\Omega$-background and with an arbitrary
simple gauge group is fully determined by studying renormalization group
equations of vevs of surface operators generating one-form symmetries. The
corresponding system of equations is a {\it non-autonomous} Toda chain, the
time being the RG scale. We obtain new recurrence relations which provide a
systematic algorithm computing multi-instanton corrections from the tree-level
one-loop prepotential as the asymptotic boundary condition of the RGE. We
exemplify by computing the $E_6$ and $G_2$ cases up to two-instantons.
