Online Multi-Object Tracking (MOT) from videos is a challenging computer vision task which has been extensively studied for decades. Most of the existing MOT algorithms are based on the Tracking-by-Detection (TBD) paradigm combined with popular machine learning approaches which largely reduce the human effort to tune algorithm parameters. However, the commonly used supervised learning approaches require the labeled data (e.g., bounding boxes), which is expensive for videos. Also, the TBD framework is usually suboptimal since it is not end-to-end, i.e., it considers the task as detection and tracking, but not jointly. To achieve both label-free and end-to-end learning of MOT, we propose a Tracking-by-Animation framework, where a differentiable neural model first tracks objects from input frames and then animates these objects into reconstructed frames. Learning is then driven by the reconstruction error through backpropagation. We further propose a Reprioritized Attentive Tracking to improve the robustness of data association. Experiments conducted on both synthetic and real video datasets show the potential of the proposed model.