Training Deep Neural Networks (DNN) concurrently is becoming increasingly important for deep learning practitioners, e.g.,hyperparameter optimization (HPO)andneural architecture search (NAS). The GPU memory capacity is the impediment that prohibits multiple DNNs from being trained on the same GPU due to the large memory usage during training. In this paper, we proposeWaterwave, a GPU memory flow engine for concurrent deep learning training. First, to address the memory explosion brought by the long time lag between memory allocation and deallocation time, we develop an allocator tailored for multi-streams. By making the allocator aware of the stream information, aprioritized allocationis conducted based on the chunk'ssynchronizationattributes, allowing us to provide useable memory after scheduling rather than waiting it to be really released after GPU computation. Second,Waterwavepartitions the compute graph to a set of continuousnode groupsand then performs finer-grained scheduling:NodeGroup pipeline execution, to guarantee a proper memory requests order.Waterwavecan accomplish up to 96.8% of the maximum batch size of solo training. Additionally, in scenarios with high memory demand,Waterwavecan outperform existing spatial sharing and temporal sharing by up to 12x and 1.49x, respectively.