Joan Bruna is a co-author in this preprint , introducing Stochastic Optimal Control Matching (SOCM), a novel Iterative Diffusion Optimization (IDO) technique for stochastic optimal control. Stochastic optimal control’s goal is to drive the behavior of noisy systems. In this work, the control is learned via a least squares problem by trying to fit a matching vector field. The key idea underlying SOCM is the path-wise reparameterization trick, a novel technique that is of independent interest, e.g., for generative modeling. The code can be found on github .