This paper proposes a novel pan-sharpening method called PIF-Net, which aims to progressively restore high-frequency signals of varying scales in the multi-spectral (MS) image in the implicit space. The method addresses the challenge of deep neural networks (DNNs) prioritizing low-frequency components during training, which limits the restoration of high-frequency edge details in MS images. To overcome this, the paper treats pan-sharpening as a coarse-to-fine high-frequency restoration problem and proposes a novel method for achieving high-quality restoration of edge information in MS images. The method introduces a Band-limited Multi-scale High-frequency Generator (BMHG) to generate high-frequency signals from the PAN image within different bandwidths. This allows for the progressive injection of higher-frequency signals into the MS image during training, enabling gradients to flow smoothly from later to earlier blocks, encouraging intermediate blocks to focus on missing details. Additionally, a Spatial-spectral Implicit Image Function (SIIF) is designed to effectively represent and fuse spatial and spectral features in the continuous domain, addressing the issue of pixel position misalignment arising from multi-scale features fusion. Extensive experiments on three satellite datasets demonstrate that the proposed method outperforms existing approaches in terms of quantitative and visual measurements for high-frequency detail recovery. The method achieves superior performance in terms of PSNR, SSIM, SAM, and ERGAS metrics, as well as in visual comparisons with state-of-the-art methods. Ablation studies further confirm the effectiveness of the BMHG, SIIF, and Progressive High-frequency Injection Module (PHIM) in the network. The paper concludes that the proposed method provides a more effective solution for pan-sharpening by leveraging implicit neural representations and a progressive strategy for high-frequency signal restoration. The method is evaluated on real-world datasets and shows significant improvements in image quality and generalization ability.This paper proposes a novel pan-sharpening method called PIF-Net, which aims to progressively restore high-frequency signals of varying scales in the multi-spectral (MS) image in the implicit space. The method addresses the challenge of deep neural networks (DNNs) prioritizing low-frequency components during training, which limits the restoration of high-frequency edge details in MS images. To overcome this, the paper treats pan-sharpening as a coarse-to-fine high-frequency restoration problem and proposes a novel method for achieving high-quality restoration of edge information in MS images. The method introduces a Band-limited Multi-scale High-frequency Generator (BMHG) to generate high-frequency signals from the PAN image within different bandwidths. This allows for the progressive injection of higher-frequency signals into the MS image during training, enabling gradients to flow smoothly from later to earlier blocks, encouraging intermediate blocks to focus on missing details. Additionally, a Spatial-spectral Implicit Image Function (SIIF) is designed to effectively represent and fuse spatial and spectral features in the continuous domain, addressing the issue of pixel position misalignment arising from multi-scale features fusion. Extensive experiments on three satellite datasets demonstrate that the proposed method outperforms existing approaches in terms of quantitative and visual measurements for high-frequency detail recovery. The method achieves superior performance in terms of PSNR, SSIM, SAM, and ERGAS metrics, as well as in visual comparisons with state-of-the-art methods. Ablation studies further confirm the effectiveness of the BMHG, SIIF, and Progressive High-frequency Injection Module (PHIM) in the network. The paper concludes that the proposed method provides a more effective solution for pan-sharpening by leveraging implicit neural representations and a progressive strategy for high-frequency signal restoration. The method is evaluated on real-world datasets and shows significant improvements in image quality and generalization ability.