With the advances in smart sensing and data mining technologies of Industry 4.0, condition monitoring of key equipment in manufacturing has brought transformations in production and maintenance management. However, in practical applications, noise from both the working environment and the sensing devices is inevitable, which causes the low performance of data-driven fault diagnosis. To address this challenge, the paper develops a robust two-stage joint denoising method by integrating ensemble empirical mode decomposition (EEMD) and independent component analysis (ICA), with fuzzy entropy discriminant as a threshold. The developed method can filter noisy components from decomposed modal components and reconstruct a new signal with denoised independent components. Moreover, an improved convolutional neural network (CNN) model based on the VGG structure has been constructed as a classifier to achieve end-to-end fault diagnosis. The experimental results demonstrate the high accuracy and superior anti-interference capability of the proposed method for rolling bearing fault diagnosis under various noise levels. Compared with state-of-the-art denoising methods and fault diagnosis methods, the proposed method achieves higher accuracy and robustness under variable noise interference. The proposed method can be applied to broader fault diagnosis tasks of production equipment in complex practical environments