  We propose a unifying approach that starts from the perturbative construction
of trivializing maps by L\"uscher and then improves on it by learning. The
resulting continuous normalizing flow model can be implemented using common
tools of lattice field theory and requires several orders of magnitude fewer
parameters than any existing machine learning approach. Specifically, our model
can achieve competitive performance with as few as 14 parameters while existing
deep-learning models have around 1 million parameters for $SU(3)$ Yang--Mills
theory on a $16^2$ lattice. This has obvious consequences for training speed
and interpretability. It also provides a plausible path for scaling
machine-learning approaches toward realistic theories.
