Large deep learning models have demonstrated strong ability to solve many tasks across a wide range of applications. Those large models typically require training and inference to be distributed. Tensor parallelism is a common technique partitioning computation of an operation or layer across devices to overcome the memory capacity limitation of a single processor, and/or to accelerate computation to meet a certain latency requirement. However, this kind of parallelism introduces additional communication that might contribute a significant portion of overall runtime. Thus limits scalability of this technique within a group of devices with high speed interconnects, such as GPUs with NVLinks in a node. This paper proposes a novel method, Flux, to significantly hide communication latencies with dependent computations for GPUs. Flux over-decomposes communication and computation operations into much finer-grained operations and further fuses them into a larger kernel to effectively hide communication without compromising kernel efficiency. Flux can potentially overlap up to 96% of communication given a fused kernel. Overall, it can achieve up to 1.24x speedups for training over Megatron-LM on a cluster of 128 GPUs with various GPU generations and interconnects, and up to 1.66x and 1.30x speedups for prefill and decoding inference over vLLM on a cluster with 8 GPUs with various GPU generations and interconnects.