In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues.We propose a novel conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene.We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible.Furthermore, leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA game, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance, generating diverse trajectories that are physically and socially plausible.Moreover, the one-step student model is significantly faster than the teacher flow model in sampling.