<p>Microscopes face a trade-off between spatial resolution, field of view and frame rate—improving one of these properties typically requires sacrificing others, owing to the limited spatiotemporal throughput of the sensor. To overcome this, we propose a new microscope that achieves snapshot gigapixel-scale imaging with a sensor array and a diffractive optical element. We improve spatiotemporal throughput in two ways. First, we capture data with an array of 48 sensors, resulting in 48× more pixels than a single sensor. Second, we use point spread function engineering and compressive sensing algorithms to fill in the missing information from the gaps between the individual sensors in the array, further increasing the spatiotemporal throughput of the system by an additional &gt;5.4×. The array of sensors is modelled as a single large-format ‘super sensor’, with erasures corresponding to the gap areas between sensors. The sensor array is placed at the output of a (nearly) 4<i>f</i> imaging system, with a diffractive optical element in the Fourier plane that generates a distributed multi-spot point spread function. This enables encoding of information from the entire super-sensor area, including the gaps. We then perform a large-scale regularized reconstruction using a direct fully shift-variant convolutional forward model, assuming that the object is sparse in some domain. Our microscope can achieve ~3 μm resolution over &gt;5.2 cm² field of view at up to 120 fps, culminating in an effective total spatiotemporal throughput of 25.2 billion pixels per second. We demonstrate the versatility of our microscope in two different modes: structural imaging via dark-field contrast and functional fluorescence imaging of calcium dynamics across dozens of freely moving <i>Caenorhabditis elegans</i>.</p>