Communication compression is a crucial technique for modern distributed learning systems to alleviate their communication bottlenecks over slower networks. Despite recent intensive studies of gradient compression for data parallel-style training, compressing the activations for models trained with pipeline parallelism is still an open problem. In this paper, we propose AC-SGD, a novel activation compression algorithm for communication-efficient pipeline parallelism training over slow networks. Different from previous efforts in activation compression, instead of compressing activation values directly, AC-SGD compresses the changes of the activations. This allows us to show, to the best of our knowledge for the first time, that one can still achieve $O(1/\sqrt{T})$ convergence rate for non-convex objectives under activation compression, without making assumptions on gradient unbiasedness that do not hold for deep learning models with non-linear activation functions.We then show that AC-SGD can be optimized and implemented efficiently, without additional end-to-end runtime overhead.We evaluated AC-SGD to fine-tune language models with up to 1.5 billion parameters, compressing activations to 2-4 bits.AC-SGD provides up to 4.3X end-to-end speed-up in slower networks, without sacrificing model quality. Moreover, we also show that AC-SGD can be combined with state-of-the-art gradient compression algorithms to enable "end-to-end communication compression: All communications between machines, including model gradients, forward activations, and backward gradients are compressed into lower precision.This provides up to 4.9X end-to-end speed-up, without sacrificing model quality.