Future frame prediction in videos is a promising avenue for unsupervised video representation learning. Video frames are naturally generated by the inherent pixel flows from preceding frames based on the appearance and motion dynamics in the video. However, existing methods focus on directly hallucinating pixel values, resulting in blurry predictions. In this paper, we develop a dual motion Generative Adversarial Net (GAN) architecture, which learns to explicitly enforce future-frame predictions to be consistent with the pixel-wise flows in the video through a dual-learning mechanism. The primal future-frame prediction and dual future-flow prediction form a closed loop, generating informative feedback signals to each other for better video prediction. To make both synthesized future frames and flows indistinguishable from reality, a dual adversarial training method is proposed to ensure that the future-flow prediction is able to help infer realistic future-frames, while the future-frame prediction in turn leads to realistic optical flows. Our dual motion GAN also handles natural motion uncertainty in different pixel locations with a new probabilistic motion encoder, which is based on variational autoencoders. Extensive experiments demonstrate that the proposed dual motion GAN significantly outperforms state-of-the-art approaches on synthesizing new video frames and predicting future flows. Our model generalizes well across diverse visual scenes and shows superiority in unsupervised video representation learning.