This paper proposes a novel fault diagnosis method that integrates a Relative Position Matrix (RPM), a Downsampling Attention Module (DAM), an Improved Residual Network (IResNet), and transfer learning to address the challenges of scarce fault data and poor generalization under variable working conditions. The RPM converts 1D vibration signals into 2D images to enhance feature representation. The DAM achieves lossless feature compression and selection via Haar wavelet downsampling and convolutional attention. An IResNet then performs deep feature learning and classification. A transfer learning strategy further enables effective knowledge adaptation from data-rich source domains to data-scarce target domains, significantly improving performance in cross-condition and small-sample scenarios. Experiments on multiple bearing and gear datasets demonstrate that the proposed method achieves over 99.5% accuracy, with 100% in key transfer tasks, outperforming existing state-of-the-art approaches. The main contributions of this work include the unified RPM-DAM-IResNet framework, a targeted small-sample transfer strategy, and comprehensive validation of its superior accuracy and robustness.