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We study a novel and important communication pattern in large-scale model-parallel deep learning (DL), which we call cross-mesh resharding. This pattern emerges when the two paradigms of model parallelism - intra-operator and inter-operator parallelism - are combined to support large models on large clusters. In cross-mesh resharding, a sharded tensor needs to be sent from a source device mesh to a destination device mesh, on which the tensor may be distributed with the same or different layouts. We formalize this as a many-to-many multicast communication problem, and show that existing approaches either are sub-optimal or do not generalize to different network topologies or tensor layouts, which result from different model architectures and parallelism strategies. We then propose two contributions to address cross-mesh resharding: an efficient broadcast-based communication system, and an "overlapping-friendly" pipeline schedule. On microbenchmarks, our overall system outperforms existing ones by up to 10x across various tensor and mesh layouts. On end-to-end training of two large models, GPT-3 and U-Transformer, we improve throughput by 10% and 50%, respectively.