Weakly supervised object detection and semanticsegmentation with image-level annotations have attracted ex-tensive attention due to their high label efficiency. Multipleinstance learning (MIL) offers a feasible solution forthe twotasks by treating each image as a bag with a series of instances(object regions or pixels) and identifying foreground instancesthat contribute to bag classification. However, conventional MILparadigms often suffer from issues, e.g., discriminative instancedomination and missing instances.In this paper, weobservethat negative instances usually contain valuable deterministicinformation, which is the key to solving the two issues. Motivatedby this, we proposea novel MIL paradigm based on negativedeterministic information (NDI), termed NDI-MIL, whichisbased on two core designs with a progressive relation: NDIcollection and negative contrastive learning. In NDI collection,we identify and distill NDI from negative instances online bya dynamic feature bank. The collected NDI is then utilized ina negative contrastive learning mechanism to locate and punishthose discriminative regions, by which the discriminative instancedomination and missing instances issues are effectively addressed,leading to improved object- and pixel-level localization accuracyand completeness. In addition, we design an NDI-guided instanceselection strategy to further enhance the systematic performance.Experimental results on several public benchmarks, includingPASCAL VOC 2007, PASCAL VOC 2012, and MS COCO, showthat our method achieves satisfactory performance. The code isavailable at: https://github.com/GC-WSL/NDI.</p