Flood detection from synthetic aperture radar (SAR) imagery plays an important role in crisis and disaster management. Based on pre- and post-flood SAR images, flooded areas can be extracted by detecting changes of water bodies. Existing state-of-the-art change detection methods primarily target optical image pairs. The nature of SAR images, such as scarce visual information, similar backscatter signals, and ubiquitous speckle noise, pose great challenges to identifying water bodies and mining change features, thus resulting in unsatisfactory performance. Besides, the lack of large-scale annotated datasets hinders the development of accurate flood detection methods. In this paper, we focus on the difference between SAR image pairs and present a differential attention metric-based network (DAM-Net), to achieve flood detection. By introducing feature interaction during temporal-wise feature representation, we guide the model to focus on changes of interest rather than fully understanding the scene of the image. On the other hand, we devise a class token to capture high-level semantic information about water body changes, increasing the ability to distinguish water body changes and pseudo changes caused by similar signals or speckle noise. To better train and evaluate DAM-Net, we create a large-scale flood detection dataset using Sentinel-1 SAR imagery, namely S1GFloods. This dataset consists of 5,360 image pairs, covering 46 flood events during 2015–2022, and spanning 6 continents of the world. The experimental results on this dataset demonstrate that our method outperforms several advanced change detection methods. DAM-Net achieves 97.8% overall accuracy, 96.5% F1, and 93.2% IoU on the test set. Our dataset and code are available at https://github.com/Tamer-Saleh/S1GFlood-Detection.