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Instance segmentation in videos, which aims to segment and track multiple objects in video frames, has garnered a flurry of research attention in recent years. In this paper, we present a novel weakly supervised framework with \textbf{S}patio-\textbf{T}emporal \textbf{C}ollaboration for instance \textbf{Seg}mentation in videos, namely \textbf{STC-Seg}. Concretely, STC-Seg demonstrates four contributions. First, we leverage the complementary representations from unsupervised depth estimation and optical flow to produce effective pseudo-labels for training deep networks and predicting high-quality instance masks. Second, to enhance the mask generation, we devise a puzzle loss, which enables end-to-end training using box-level annotations. Third, our tracking module jointly utilizes bounding-box diagonal points with spatio-temporal discrepancy to model movements, which largely improves the robustness to different object appearances. Finally, our framework is flexible and enables image-level instance segmentation methods to operate the video-level task. We conduct an extensive set of experiments on the KITTI MOTS and YT-VIS datasets. Experimental results demonstrate that our method achieves strong performance and even outperforms fully supervised TrackR-CNN and MaskTrack R-CNN. We believe that STC-Seg can be a valuable addition to the community, as it reflects the tip of an iceberg about the innovative opportunities in the weakly supervised paradigm for instance segmentation in videos.