Real-time, high-fidelity monocular depth estimation from remote sensing imagery is crucial for numerous applications, yet existing methods face a stark trade-off between accuracy and efficiency. Although using Vision Transformer (ViT) backbones for dense prediction is fast, they often exhibit poor perceptual quality. Conversely, diffusion models offer high fidelity but at a prohibitive computational cost. To overcome these limitations, we propose Depth Detail Diffusion for Remote Sensing Monocular Depth Estimation ($D^3$-RSMDE), an efficient framework designed to achieve an optimal balance between speed and quality. Our framework first leverages a ViT-based module to rapidly generate a high-quality preliminary depth map construction, which serves as a structural prior, effectively replacing the time-consuming initial structure generation stage of diffusion models. Based on this prior, we propose a Progressive Linear Blending R}efinement (PLBR) strategy, which uses a lightweight U-Net to refine the details in only a few iterations. The entire refinement step operates efficiently in a compact latent space supported by a Variational Autoencoder (VAE). Extensive experiments demonstrate that $D^3$-RSMDE achieves a notable 11.85\% reduction in the Learned Perceptual Image Patch Similarity (LPIPS) perceptual metric over leading models like Marigold, while also achieving over a 40$\times$ speedup in inference and maintaining VRAM usage comparable to lightweight ViT models. Our project is available at https://anonymous.4open.science/r/D3RSMDE-5547.