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Existing deep learning systems commonly parallelize deep neural network (DNN) training using data or model parallelism, but these strategies often result in suboptimal parallelization performance. We introduce SOAP, a more comprehensive search space of parallelization strategies for DNNs that includes strategies to parallelize a DNN in the Sample, Operator, Attribute, and Parameter dimensions. We present FlexFlow, a deep learning engine that uses guided randomized search of the SOAP space to find a fast parallelization strategy for a specific parallel machine. To accelerate this search, FlexFlow introduces a novel execution simulator that can accurately predict a parallelization strategy’s performance and is three orders of magnitude faster than prior approaches that execute each strategy. We evaluate FlexFlow with six real-world DNN benchmarks on two GPU clusters and show that FlexFlow increases training throughput by up to 3.3× over state-of-the-art approaches, even when including its search time, and also improves scalability.