Multi-source fault features in the electric drive systems of tunnel boring machines (TBMs) are susceptible to aliasing, while single-task models struggle to balance diagnostic accuracy and reliability under multi-motor coordination, non-stationary loads, and strong background noise. To address these challenges, a multi-task fault diagnosis method based on an adaptive sparse fusion network is proposed. First, current, torque, and temperature signals are denoised using wavelet thresholding, after which their time- and frequency-domain features are extracted and normalized. Learnable modality weights are then introduced to enable task-oriented adaptive fusion of multi-source features. Task-gradient cosine similarity is used to identify conflict relationships, and dynamic sparse masks are applied to isolate conflicting tasks while enabling parameter sharing among collaborative tasks. Finally, quantile regression is employed to estimate the upper and lower bounds of temperature variation, forming an auxiliary module for temperature anomaly detection. Using monitoring data collected from a TBM operating in a high-altitude, long-distance rock tunnel in China, a dataset comprising 7 200 short- and open-circuit events is created. Open-circuit fault samples are constructed and divided into training, validation, and test sets at a ratio of 7:2:1. The complete model achieves diagnostic accuracies of 98.89% and 99.44% for inter-turn short-circuit and inverter open-circuit faults, respectively, representing improvements of 13.89% and 14.44% over a multi-task convolutional neural network baseline without data preprocessing. Additionally, the fitted temperature-variation bounds provide interpretable thresholds for detecting temperature anomalies. These results demonstrate that the proposed method effectively improves signal quality and multimodal feature representation, mitigates gradient conflicts among tasks, and enables collaborative diagnosis of two typical electric drive system faults alongside temperature anomaly detection.