Change Detection (CD) enables the identification of alterations between images of the same area captured at different times. However, existing CD methods still struggle to address pseudo changes resulting from domain information differences in multi-temporal images and instances of detail errors caused by the loss and contamination of detail features during the upsampling process in the network. To address this, we propose a bi-temporal Gaussian distribution feature-dependent network (BGFD). Specifically, we first introduce the Gaussian noise domain disturbance (GNDD) module, which approximates distribution using image statistical features to characterize domain information, samples noise to perturb the network for learning redundant domain information, addressing domain information differences from a more fundamental perspective. Additionally, within the feature dependency facilitation (FDF) module, we integrate a novel mutual information difference loss ($L_{MI}$) and more sophisticated attention mechanisms to enhance the capabilities of the network, ensuring the acquisition of essential domain information. Subsequently, we have designed a novel detail feature compensation (DFC) module, which compensates for detail feature loss and contamination introduced during the upsampling process from the perspectives of enhancing local features and refining global features. The BGFD has effectively reduced pseudo changes and enhanced the detection capability of detail information. It has also achieved state-of-the-art performance on four publicly available datasets - DSIFN-CD, SYSU-CD, LEVIR-CD, and S2Looking, surpassing baseline models by +8.58%, +1.28%, +0.31%, and +3.76% respectively, in terms of the F1-Score metric.