Big data and artificial intelligence (AI) methods are revolutionizing how knowledge is gained and predictions are made for sustainability sciences and the global environment. AI methods, especially deep networks, have strong predictive skills yet have restricted interpretability and limitations for unseen extremes. Here we show that differentiable models (a genre of physics-informed machine learning where gradients can be rapidly computed via a range of methods such as automatic differentiation, allowing process-based equations to be seamlessly connected to neural networks, https://t.co/qyuAzYPA6Y) are well-suited to capture unseen extremes because they preserve physical principles like mass balances and first-order exchanges and restrict the role of neural networks. Based on benchmarks for both the continental United States and global datasets, we found our differentiable model (called δHBV) can even outperform long short-term memory (LSTM) networks for unseen events with a return period of 5 years or more. This advantage was more pronounced as the return period increased. A multiscale parameterization approach, differentiable flood routing, and careful use of dynamical parameterization further improved the performance for flood extremes on large rivers.