Perception and prediction are two separate modules in the existing autonomous driving systems. They interact with each other via hand-picked features such as agent bounding boxes and trajectories. Due to this separation, prediction, as a downstream module, only receives limited information from the perception module. To make matters worse, errors from the perception modules can propagate and accumulate, adversely affecting the prediction results. In this work, we propose ViP3D, a query-based visual trajectory prediction pipeline that exploits rich information from raw videos to directly predict future trajectories of agents in a scene. ViP3D employs sparse agent queries to detect, track, and predict throughout the pipeline, making it the first fully differentiable vision-based trajectory prediction approach. Instead of using historical feature maps and trajectories, useful information from previous timestamps is encoded in agent queries, which makes ViP3D a concise streaming prediction method. Furthermore, extensive experimental results on the nuScenes dataset show the strong vision-based prediction performance of ViP3D over traditional pipelines and previous end-to-end models.