Training modern deep neural network (DNN) models involves complex workflows triggered by model exploration, sensitivity analysis, explainability, etc. A key primitive in this context is the ability to clone a model training instance, i.e. "fork" the training process in a potentially different direction, which enables comparisons of different evolution paths using variations of training data and model parameters. However, in a quest improve the training throughput, a mix of data parallel, model parallel, pipeline parallel and layer-wise parallel approaches are making the problem of cloning highly complex. In this paper, we explore the problem of efficient cloning under such circumstances. To this end, we leverage several properties of dataparallel training and layer-wise parallelism to design DeepClone, a cloning approach based on augmenting the execution graph to gain direct access to tensors, which are then sharded and reconstructed asynchronously in order to minimize runtime overhead, standby duration, readiness duration. Compared with state-of-art approaches, DeepClone shows orders of magnitude improvement for several classes of DNN models.