Generating coherent and natural movement is the key challenge in video generation. This research proposes to condense video generation into a problem of motion generation, to improve the expressiveness of motion and make video generation more manageable. This can be achieved by breaking down the video generation process into latent motion generation and video reconstruction. We present a latent motion diffusion (LaMD) framework, which consists of a motion-decomposed video autoencoder and a diffusion-based motion generator, to implement this idea. Through careful design, the motion-decomposed video autoencoder can compress patterns in movement into a concise latent motion representation. Meanwhile, the diffusion-based motion generator is able to efficiently generate realistic motion on a continuous latent space under multi-modal conditions, at a cost that is similar to that of image diffusion models. Results show that LaMD generates high-quality videos with a wide range of motions, from stochastic dynamics to highly controllable movements. It achieves new state-of-the-art performance on benchmark datasets, including BAIR, Landscape and CATER-GENs, for Image-to-Video (I2V) and Text-Image-to-Video (TI2V) generation. The source code of LaMD will be made available soon.