用几何对称性和奇异值门控实现无数据图像修复，零样本效果领先。
SE-UNet: Singular Equivariant Imaging for Real-World Constrained Generation
- 通过D4对称性与奇异值门控约束生成过程，构建强先验优化框架。
- 在CIFAR-10上实现80%缺失像素的零样本修复，PSNR超DIP基准4 dB以上。
- 适合资源受限场景下的图像重建，尤其适用于物理约束强的任务。
尽管扩散模型革新了图像生成，但其在真实世界逆问题中的应用常受限于海量数据需求及严格物理约束难以施加。本文提出SE-UNet（奇异等变UNet），一种无需大量预训练即可解决病态成像任务的框架。通过将生成视为受几何等变性（D₄群）和奇异值门控约束的优化问题，SE-UNet有效规范解空间。实验表明，该方法在CIFAR-10上实现了80%缺失像素的零样本修补，PSNR优于深度图像先验（DIP）基线超过4 dB，且呈现“奇异快锁”收敛特性——快速锁定到信号流形。此方法为受限生成提供了高效路径，契合ReALM-GEN中理论先验与实际部署的融合目标。
原文摘要 · Abstract (English)
While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce \textbf{SE-UNet} (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance ($D_4$ group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80\% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence -- rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.
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