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 measure, in 2 or 3 spatial dimensions. The proof relies on Hairer’s theory of regularity structures, together with some insights on the interplay between gauge symmetry, regularization and renormalization. Based on [S. arXiv:1801.04596] and [Chandra,Hairer,S. work in progress].