Quantum Yang-Mills is a measure on a certain class of "connections". Its mathematical construction is well-known challenging problem. Motivated by this, we construct a stochastic dynamic associated to the (formal) measure, in 2 or 3 spatial dimensions. The proof relies on Hairer’s theory of regularity structures, together with some new observations on the interplay between gauge symmetry, regularization and renormalization. Based on [Shen, arXiv:1801.04596] and [Chandra, Hairer, Shen, work in progress].