Laser welding is a key technology for many industrial applications. However, its online quality monitoring is an open issue due to the highly complex nature of the process. This work aims at enriching existing approaches in this field. We propose a method for real-time detection of process instabilities that can lead to defects. Hard X-ray radiography is used for the ground truth observations of the sub-surface events that are critical for the quality. A deep artificial neural network is applied to reveal the unique signatures of those events in wavelet spectrograms from the laser back-reflection and acoustic emission signals. The autonomous classification of the revealed signatures is tested on real-life data, while the real-time performance is reached by means of parallel computing. The confidence of the quality classification ranges between 71% and 99%, with a temporal resolution down to 2 ms and a computation time per classification task as low as 2 ms. This approach is a new paradigm in the digitization of industrial processes and can be exploited to provide feedbacks in a closed-loop quality control system.