Calcium imaging is a key method to record patterns of neuronal activity across populations of identified neurons. Inference of temporal patterns of action potentials (‘spikes’) from calcium signals is, however, challenging and often limited by the scarcity of ground truth data containing simultaneous measurements of action potentials and calcium signals. To overcome this problem, we compiled a large and diverse ground truth database from publicly available and newly performed recordings. This database covers various types of calcium indicators, cell types, and signal-to-noise ratios and comprises a total of >20 hours from 225 neurons. We then developed a novel algorithm for spike inference (CASCADE) that is based on supervised deep networks, takes advantage of the ground truth database, infers absolute spike rates, and outperforms existing model-based algorithms. To optimize performance for unseen imaging data, CASCADE retrains itself by resampling ground truth data to match the respective sampling rate and noise level. As a consequence, no parameters need to be adjusted by the user. To facilitate routine application of CASCADE we developed systematic performance assessments for unseen data, we openly release all resources, and we provide a user-friendly cloud-based implementation.