  We introduce Wilson-It\^o diffusions, a class of random fields on
$\mathbb{R}^d$ that change continuously along a scale parameter via a Markovian
dynamics with local coefficients. Described via forward-backward stochastic
differential equations, their observables naturally form a pre-factorization
algebra \`a la Costello-Gwilliam. We argue that this is a new non-perturbative
quantization method applicable also to gauge theories and independent of a
path-integral formulation. Whenever a path-integral is available, this approach
reproduces the setting of Wilson-Polchinski flow equations.
