利用圖像的自相似性是單圖像超解析度（SISR）的關鍵，然而當前主流架構存在根本性限制：卷積神經網路（CNNs）受限於局部感受野，而 Vision Transformers 與 Mambas 等全域模型則因其一維序列扁平化的處理方式，破壞了捕捉幾何對稱性所必需的二維空間結構。我們為此提出深度摺紙網路（DON），一個嵌入了二面體群 $D_4$ 幾何先驗的新範式。其核心為一個模型無關的摺紙網路（ON）模組，它透過模擬摺紙操作，遞迴地聚合遠距離的對稱圖像塊。當 ON 與任何全域骨幹網路整合時，能賦予模型強大的二維幾何感知能力，從而能夠捕捉廣義的自相似性。我們進一步建立了層級式主資訊（PIR）框架，此框架揭示了一個雙層級優化原則（DOP）：在輸入層級探索可重建的資訊（追求高 I-PIR），同時在學習到的特徵中最小化冗餘（追求低 F-PIR）。實驗證明，DON 模型在達到頂尖性能的同時，展現出極低的 F-PIR 值，此結果驗證了我們的理論，並實現了高效的特徵解耦。

Exploiting image self-similarity is key to Single Image Super-Resolution (SISR), yet prevailing architectures are fundamentally limited: CNNs by local receptive fields, and global models like Vision Transformers by their 1D sequence flattening, which disrupts the 2D spatial structure essential for capturing geometric symmetries. We introduce the Deep Origami Network (DON), a paradigm that embeds geometric priors from the dihedral group $D_4$. At its core, the model-agnostic Origami Network (ON) module recursively aggregates distant symmetric patches via simulated origami operations. When integrated with any global backbone, ON confers potent 2D geometric awareness, enabling the capture of generalized self-similarities. We further establish the Hierarchical Prime Information (PIR) framework, which reveals a Dual-level Optimization Principle (DOP) that explores reconstructible information at the input level (high I-PIR) while minimizing redundancy in the learned features (low F-PIR). Experiments demonstrate that DON models achieve state-of-the-art performance while exhibiting remarkably low F-PIR, validating our theory and achieving efficient feature decoupling.

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