Diagnosing lithium-ion battery degradation is challenging due to the complex, nonlinear, and path-dependent nature of the problem. Here, we develop a generalised and rapid degradation diagnostic method with a deep learning-convolutional neural network that quantifies degradation modes of batteries aged under various conditions in 0.012 s without feature engineering. Rather than performing extensive aging experiments, synthetic aging datasets for network training are generated. This dramatically lowers training cost/time, with these datasets covering almost all the aging paths, enabling a generalised degradation diagnostic framework. We show that the five thermodynamic degradation modes are correlated, and systematically elucidate their correlations. We thus propose a non-invasive comprehensive evaluation method and find the degradation diagnostic errors to be less than 1.22% for three leading commercial battery chemistries. The comparison with the traditional diagnostic methods confirms the high accuracy and fast nature of the proposed approach. Quantification of degradation modes with the partial discharge/charge data using the proposed diagnostic framework validates the real-world feasibility of this approach. This work, therefore, enables the promise of online identification of battery degradation and efficient analysis of large-data sets, unlocking potential for long lifetime energy storage systems.