How is Wilson Flow related to renormalization? I'm looking at a couple papers on Wilson Flow on the lattice and I'm not getting the connection to renormalization entirely.  In Luscher's paper on Wilson flow, he explains that the field configurations at later flow times are renormalized field configurations; However, it's not clear to me what the change in scale was.  For instance, in this study of the $O(3)$ nonlinear sigma model there is no change in the correlation length at later flow times, which would be a clear indicator that the "renormalized" fields had actually be coarse grained.
Is there something I'm missing? or is the Wilson flow not a genuine RG transformation?
 A: You are correct to suggest that the Wilson flow is not a genuine RG transformation.  Let me focus on the lattice context where we have a UV cutoff corresponding to the inverse lattice spacing $a^{-1}$.  (Let me also talk about the "gradient flow", of which the Wilson flow is the special case that results when we consider the gradient of the Wilson action.)
The gradient flow doesn't change the cutoff scale the way that an RG transformation would.  Even so it can be applied to define renormalized operators in a corresponding gradient flow renormalization scheme, where the renormalization scale is provided by (a function of) the 'flow time' $t$ (which has units of length squared).  A concrete example of this is provided in the paper by Lüscher that you mention, where he perturbatively relates the 'flowed' operator $t^2\langle E(t)\rangle$ to the MSbar-scheme renormalized coupling $g^2(\mu)$ at energy scale $\mu = 1 / \sqrt{8t}$.  This was one of the results that sparked the current interest in this technique.
If it might be useful to be more visual and less mathematical, this picture is close to the image I have in my mind describing how the renormalized operators $\cal{O}(t,x)$ are constructed by 'smoothing' (with a gaussian kernel) the original fields $\cal{O}(0,x)$ over a sphere of radius roughly $\sqrt{8t}$.  (If mathematics is better, arXiv:1308.5598 has a quick summary.  I should also point out hep-th/0601210.)  Fig. 1 of arXiv:1311.2679 might also be useful (though I wouldn't recommend the proceedings as a whole, since that project didn't progress any further).

Edit to belatedly add: "Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows" (arXiv:1806.01385, recently published in Phys.Rev.Lett.) may also be a useful reference to address this question.
