Gearbox fault diagnosis under strong-noise conditions remains challenging due to the difficulty of extracting weak fault-related features from noise-dominated vibration signals, inefficient modeling of multi-scale impulsive characteristics under limited computational resources, and degraded diagnostic stability across varying noise levels. To address these issues, this paper proposes a lightweight fault diagnosis model (DSMC-ECA) that integrates an improved multi-scale depthwise separable convolution scheme with efficient channel attention. The proposed model adopts a dual-branch parallel feature extraction architecture: the SMC branch captures local fine-grained impulsive features, while the SMDC branch expands the receptive field via multi-scale separable dilated convolutions to model long-range dependencies. Meanwhile, ECA is embedded into the multi-scale features for channel-wise recalibration, highlighting fault-relevant discriminative information and suppressing noise disturbances. The model contains only 0.204 M parameters and requires 10.037 M FLOPs, achieving a favorable trade-off between performance and efficiency. Experimental results on the XJTU and SEU datasets demonstrate that DSMC-ECA consistently outperforms baseline methods across a wide range of signal-to-noise ratios (from −6 dB to noise-free conditions). Notably, under the most challenging −6 dB setting, it achieves the highest average diagnostic accuracies of 95.11% (XJTU) and 86.84% (SEU).