Title: Continuous Propagation: Layer-Parallel Training. Abstract: Continuous propagation is a parallel technique for training deep neural networks with batch size one at full utilization of a multiprocessor system. It enables spatially distributed computations on emerging deep learning hardware accelerators that do not impose programming limitations of contemporary GPUs. The algorithm achieves model parallelism along the depth of a deep network. The method is based on the continuous representation of the optimization process and enables sustained gradient generation during all phases of computation. We demonstrate that in addition to its increased concurrency, continuous propagation improves the convergence rate of state of the art methods while matching their accuracy. 