Pipeline parallelism is one of the key components for large-scale distributed training, yet its efficiency suffers from pipeline bubbles which were deemed inevitable. In this work, we introduce a scheduling strategy that, to our knowledge, is the first to successfully achieve zero pipeline bubbles under synchronous training semantics. The key idea behind this improvement is to split the backward computation into two parts, one that computes gradient for the input and another that computes for the parameters. Based on this idea, we handcraft novel pipeline schedules that significantly outperform the baseline methods. We further develop an algorithm that automatically finds an optimal schedule based on specific model configuration and memory limit. Additionally, to truly achieve zero bubble, we introduce a novel technique to bypass synchronizations during the optimizer step. Experimental evaluations show that our method outperforms the 1F1B schedule up to 15\% in throughput under a similar memory limit. This number can be further pushed to 30\% when the memory constraint is relaxed. We believe our results mark a major step forward in harnessing the true potential of pipeline parallelism. The source code based on Megatron-LM is publicly avaiable at \url{https://github.com/sail-sg/zero-bubble-pipeline-parallelism}.