Nonpertubative renormalization in quantum field theory versus statistical physics

Question

I am trying to work my head around how renormalization works for quantum field theory. Most treatments cover perturbative renormalization theory and I am fine with this approach. But it is not the most general framework and is not intuitively related to the Wilsonian approach. I am also a bit lost with respect to the meaning of the associated notions in the QFT context like the anomalous dimension. So, I essence what I am asking what is the intuitive picture relating the coarse graining idea of statistical physics with the framework of quantum field theory. Also, how could one picture/understand the notion of proliferation, coupling constants, beta functions, fixed points, anomalous dimension and conformal invariance with respect to the way the ideas are "found" in statistical physics. I find it easy to visualize the entire procedure in the latter context but not in the former. A complete analogy might not be possible but I am only asking to what extent it can be achieved.