Remotely sensed image high-accuracy interpretation (RSIHI), including tasks such as semantic segmentation and change detection, faces the three major problems: (1) complementarity problem of spatially stationary-and-non-stationary frequency; (2) edge uncertainty problem caused by down-sampling in the encoder step and intrinsic edge noises; and (3) false detection problem caused by imagery registration error in change detection. To solve the aforementioned problems, an uncertainty-diffusion-model-based high-Frequency TransFormer network (UDHF2-Net) is the proposed for RSIHI, the superiority of which is as following: (1) a spatially-stationary-and-non-stationary high-frequency connection paradigm (SHCP) is proposed to enhance the interaction of spatially stationary and non-stationary frequency features to yield high-fidelity edge extraction result. Inspired by HRFormer, SHCP remains the high-frequency stream through the whole encoder-decoder process with parallel high-to-low frequency streams and reduces the edge loss by a downsampling operation; (2) a mask-and-geo-knowledge-based uncertainty diffusion module (MUDM) is proposed to improve the robustness and edge noise resistance. MUDM could further optimize the uncertain region to improve edge extraction result by gradually removing the multiple geo-knowledge-based noises; (3) a semi-pseudo-Siamese UDHF2-Net for change detection task is proposed to reduce the pseudo change by registration error. It adopts semi-pseudo-Siamese architecture to extract above complemental frequency features for adaptively reducing registration differencing, and MUDM to recover the uncertain region by gradually reducing the registration error besides above edge noises. Comprehensive experiments were performed to demonstrate the superiority of UDHF2-Net. Especially ablation experiments indicate the effectiveness of UDHF2-Net.