Title: Module-wise Training of Residual Networks via the Minimizing Movement Scheme. Abstract: Greedy layer-wise or module-wise training of neural networks is compelling in constrained and on-device settings, as it circumvents a number of problems of end-to-end back-propagation. However, it suffers from a stagnation problem, whereby early layers overfit and deeper layers stop increasing the test accuracy after a certain depth. We propose to solve this issue by introducing a simple module-wise regularization inspired by the minimizing movement scheme for gradient flows in distribution space. The method, which we call TRGL for Transport Regularized Greedy Learning, is particularly well-adapted to residual networks. We study it theoretically, proving that it leads to greedy modules that are regular and that successively solve the task. Experimentally, we show improved accuracy of module-wise trained networks when our regularization is added.