Implicit representation mapping (IRM) can translate image features to any continuous resolution, showcasing its potent capability for ultra-high-resolution image segmentation refinement. Current IRM-based methods for refining ultra-high-resolution image segmentation often rely on CNN-based encoders to extract image features and apply a Shared Implicit Representation Mapping Function (SIRMF) to convert pixel-wise features into segmented results. Hence, these methods exhibit two crucial limitations. Firstly, the CNN-based encoder may not effectively capture long-distance information, resulting in a lack of global semantic information in the pixel-wise features. Secondly, SIRMF is shared across all samples, which limits its ability to generalize and handle diverse inputs. To address these limitations, we propose a novel approach that leverages the newly proposed Adaptive Implicit Representation Mapping (AIRM) for ultra-high-resolution Image Segmentation. Specifically, the proposed method comprises two components: (1) the Affinity Empowered Encoder (AEE), a robust feature extractor that leverages the benefits of the transformer architecture and semantic affinity to model long-distance features effectively, and (2) the Adaptive Implicit Representation Mapping Function (AIRMF), which adaptively translates pixel-wise features without neglecting the global semantic information, allowing for flexible and precise feature translation. We evaluated our method on the commonly used ultra-high-resolution segmentation refinement datasets, i.e., BIG and PASCAL VOC 2012. The extensive experiments demonstrate that our method outperforms competitors by a large margin. The code is provided in supplementary material.