  The gradient flow bears a close resemblance to the coarse graining, the
guiding principle of the renormalization group (RG). In the case of scalar
field theory, a precise connection has been made between the gradient flow and
the RG flow of the Wilson action in the exact renormalization group (ERG)
formalism. By imitating the structure of this connection, we propose an ERG
differential equation that preserves manifest gauge invariance in Yang--Mills
theory. Our construction in continuum theory can be extended to lattice gauge
theory.
