We investigate a new task in human motion prediction, which aims to forecast future body poses from historically observed sequences while accounting for arbitrary latency. This differs from existing works that assume an ideal scenario where future motions can be instantaneously'' predicted, thereby neglecting time delays caused by network transmission and algorithm execution. Addressing this task requires tackling two key challenges: The length of latency period can vary significantly across samples; the prediction model must be efficient. In this paper, we propose ALIEN, which treats the motion as a continuous function parameterized by a neural network, enabling predictions under any latency condition. By incorporating Mamba-like linear attention as a hyper-network and designing subsequent low-rank modulation, ALIEN efficiently learns a set of implicit neural representation weights from the observed motion to encode instance-specific information. Additionally, our model integrates the primary motion prediction task with an extra-designed variable-delay pose reconstruction task in a unified multi-task learning framework, enhancing its ability to capture richer motion patterns. Extensive experiments demonstrate that our approach outperforms state-of-the-art baselines adapted for our new task, while maintaining competitive performance in traditional prediction setting.