As an important driving device, the permanent magnet synchronous motor (PMSM) plays a critical role in modern industrial fields. Given the harsh working environment, research into accurate PMSM fault diagnosis methods is of practical significance. Time–frequency analysis captures the rich features of PMSM operating conditions, and convolutional neural networks (CNNs) offer excellent feature extraction capabilities. This study proposes an intelligent fault diagnosis method based on continuous wavelet transform (CWT) and CNNs. Initially, a mechanism analysis is conducted on the inter-turn short-circuit and demagnetization faults of PMSMs, identifying and displaying the key feature frequency range in a time–frequency format. Subsequently, a CNN model is developed to extract and classify these time–frequency images. The feature extraction and diagnosis results are visualized with t-distributed stochastic neighbor embedding (t-SNE). The results demonstrate that our method achieves an accuracy rate of over 98.6% for inter-turn short-circuit and demagnetization faults in PMSMs of various severities.