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Real-time video inference on edge devices like mobile phones and drones is challenging due to the high computation cost of Deep Neural Networks. We present Adaptive Model Streaming (AMS), a new approach to improving performance of efficient lightweight models for video inference on edge devices. AMS uses a remote server to continually train and adapt a small model running on the edge device, boosting its performance on the live video using online knowledge distillation from a large, state-of-the-art model. We discuss the challenges of over-the-network model adaptation for video inference, and present several techniques to reduce communication cost of this approach: avoiding excessive overfitting, updating a small fraction of important model parameters, and adaptive sampling of training frames at edge devices. On the task of video semantic segmentation, our experimental results show 0.4--17.8 percent mean Intersection-over-Union improvement compared to a pre-trained model across several video datasets. Our prototype can perform video segmentation at 30 frames-per-second with 40 milliseconds camera-to-label latency on a Samsung Galaxy S10+ mobile phone, using less than 300 Kbps uplink and downlink bandwidth on the device.