Large-scale cyber data breach incidents have occurred frequently in recent years, posing substantial challenges to global cybersecurity and risk management systems. There is strong demand for systematic and effective approaches to modeling and pricing cyber data breach risk. Reliable prediction is mainly hindered by data sparsity,  and complex dependence patterns across time, geography, and industry sectors. We develop a two-part deep learning framework that jointly models (i) the probability of observing a breach event and (ii) the conditional distribution of loss severity given an event. The framework adopts a unified encoder--decoder architecture: an attention-based recurrent encoder learns dynamic temporal--spatial representations from historical signals, while two specialized decoders handle the zero-event component and the nonzero severity component, respectively. For severity, we employ a conditional normalizing-flow decoder to produce flexible full-distribution forecasts with improved tail behavior and calibration. In an empirical study, the proposed framework consistently outperforms classical statistical approaches and competitive deep learning baselines in distributional predictive accuracy. We further show how the resulting predictive distributions translate into insurance-relevant outputs, including portfolio-level risk measures and group- and firm-level premium indications.