To address the fault diagnosis issues of inter-winding short circuits and inter-turn short circuits in permanent magnet synchronous motors (PMSM), this paper proposes a novel dual-branch PMSM fault diagnosis model combining Residual Network (ResNet), Liquid Neural Networks (LNN), and Bidirectional Cross-Attention Mechanism (BiCA). In terms of data processing, a signal processing method integrating ICEEMDAN decomposition, Permutation Entropy (PE), and Wavelet Threshold Denoising (WTD) is proposed to effectively reduce noise interference, highlight fault characteristics of inter-winding and inter-turn short circuits, and provide effective time-domain information for the model. Meanwhile, VMD decomposition is employed to retain complete data information, offering frequency-domain features for the model. The two types of features are fed into the RES-LNN-BiCA model in parallel: the ResNet structure effectively extracts signal features and reduces the computational burden of LNN; LNN incorporates continuous-time dynamics, enabling robust temporal modeling capabilities to capture long-term dependencies in the data and perform continuous-time dynamic modeling of signals. Finally, the BiCA mechanism is introduced to cross-fuse time-domain and frequency-domain features from both branches, avoiding the one-sidedness of information from a single branch. The measured data shows that the method proposed in this paper has strong fault diagnosis capabilities, with a diagnostic accuracy of 99.92% in a noise free environment and an accuracy of over 95% in a noisy environment. This provides a foundation for subsequent motor fault diagnosis and liquid neural network research.