Title: Single-Stage Open-world Instance Segmentation with Cross-task Consistency Regularization. Abstract: Open-World Instance Segmentation (OWIS) is an emerging research topic that aims to segment class-agnostic object instances from images. The mainstream approaches use a two-stage segmentation framework, which first locates the candidate object bounding boxes and then performs instance segmentation. In this work, we instead promote a single-stage framework for OWIS. We argue that the end-to-end training process in the single-stage framework can be more convenient for directly regularizing the localization of class-agnostic object pixels. Based on the single-stage instance segmentation framework, we propose a regularization model to predict foreground pixels and use its relation to instance segmentation to construct a cross-task consistency loss. We show that such a consistency loss could alleviate the problem of incomplete instance annotation -- a common problem in the existing OWIS datasets. We also show that the proposed loss lends itself to an effective solution to semi-supervised OWIS that could be considered an extreme case that all object annotations are absent for some images. Our extensive experiments demonstrate that the proposed method achieves impressive results in both fully-supervised and semi-supervised settings. Compared to SOTA methods, the proposed method significantly improves the $AP_{100}$ score by 4.75\% in UVO$\rightarrow$UVO setting and 4.05\% in COCO$\rightarrow$UVO setting. In the case of semi-supervised learning, our model learned with only 30\% labeled data, even outperforms its fully-supervised counterpart with 50\% labeled data. The code will be released soon.