The so-called gradient flow, a gauge covariant diffusion of the gauge field, bears a close resemblance to the coarse graining involved in the Wilsonian renormalization group (RG). In scalar field theory, a precise connection between the gradient flow and the Wilsonian RG flow can be made. By imitating the structure of this connection, we propose a Wilsonian RG equation that preserves manifest gauge invariance in vector-like gauge theory. I also mention some ongoing studies on the basis of this formulation.