Visualizing dynamic processes over large, three-dimensional fields of view at high speed is essential for many applications in the life sciences. Light-field microscopy (LFM) has emerged as a tool for fast volumetric image acquisition, but its effective throughput and widespread use in biology has been hampered by a computationally demanding and artifact-prone image reconstruction process. Here, we present a framework for artificial intelligence-enhanced microscopy, integrating a hybrid light-field light-sheet microscope and deep learning-based volume reconstruction. In our approach, concomitantly acquired, high-resolution two-dimensional light-sheet images continuously serve as training data and validation for the convolutional neural network reconstructing the raw LFM data during extended volumetric time-lapse imaging experiments. Our network delivers high-quality three-dimensional reconstructions at video-rate throughput, which can be further refined based on the high-resolution light-sheet images. We demonstrate the capabilities of our approach by imaging medaka heart dynamics and zebrafish neural activity with volumetric imaging rates up to 100 Hz.