低秩残差扩散模型
Low-Rank Residual Diffusion Models
把扩散过程约束在低秩残差子空间里，并让前向低秩、反向满秩，这种非对称扩散设计可直接迁移到去雨、去模糊等近域复原任务，用来降低采样不确定性并保住结构细节。
原文依据 we propose the Low-Rank Residual Diffusion Model (LRDM), which performs diffusion within a compact low-rank residual subspace
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论残差扩散模型在图像复原任务中已取得显著进展。然而，在图像去雨这类近域变换中，我们观察到残差呈现出固有的低秩结构。受这一性质启发，我们提出低秩残差扩散模型（LRDM），在紧凑的低秩残差子空间内执行扩散，从而实现高效且保持结构的复原。我们将这一观察形式化为低秩残差假设，并证明当残差位于低秩空间时，变分下界会变得更紧。基于这一洞见，我们引入非对称残差扩散过程，在前向过程中将扩散约束于低秩域，同时在反向过程中保持满秩的灵活性。为适应不同扩散时间步上残差复杂度的变化，我们进一步引入自适应秩选择机制，在扩散过程中动态调整秩。在去雨、去模糊与去阴影基准上的实验表明，LRDM 超越了满秩扩散基线并达到最优性能，验证了在低秩残差空间中建模扩散的优势。项目主页：https://github.com/JF-Tan/LRDM 。
英文原文摘要 1326 字符
Residual diffusion models have achieved remarkable progress in image restoration tasks. In near-domain transformations such as image deraining, however, we observe that the residuals exhibit an inherent low-rank structure. Motivated by this property, we propose the Low-Rank Residual Diffusion Model (LRDM), which performs diffusion within a compact low-rank residual subspace for efficient and structure-preserving restoration. We formalize this observation as the Low-Rank Residual Assumption and show that the variational lower bound becomes tighter when residuals lie in a low-rank space. Building on this insight, we introduce an Asymmetric Residual Diffusion Process that constrains the forward process in the low-rank domain while maintaining full-rank flexibility in the reverse process. To accommodate the varying complexity of residuals across diffusion timesteps, we further introduce an Adaptive Rank Selection mechanism that dynamically adjusts the rank during the diffusion process. Experiments on deraining, deblurring, and deshading benchmarks show that LRDM surpasses full-rank diffusion baselines and achieves state-of-the-art performance, validating the advantage of modeling diffusion in a low-rank residual space. Project Page: \urlstyle same \hypersetup allcolors=magenta https://github.com/JF-Tan/LRDM .