<p>Computational microscopy combines advances in optical hardware and signal processing to push the boundaries of imaging resolution and functionality. However, acquiring extended information often comes at the expense of temporal resolution. Here, we present a model-based deep learning framework for time-resolved imaging in multi-shot computational microscopy. Building upon the plug-and-play (PnP) optimization theory, our approach integrates the low-level spatiotemporal priors learned from large-scale video datasets with the physical model of an optimized measurement scheme, enabling accurate, time-resolved reconstruction of dynamic scenes. Using lensless coded ptychographic microscopy as an example, we experimentally demonstrate high-speed holographic imaging of an order of magnitude faster sample dynamics without compromising quality. Additionally, we show that the proposed framework enables high-throughput, label-free imaging of various biological activities of freely moving organisms, such as paramecia and rotifers, with a sensor-limited space-bandwidth-time product of 227 megapixels per second. The presented approach provides a promising solution to time-resolved computational microscopy across a broad range of imaging modalities.</p>