Domain alignment refers broadly to learning correspondences between data distributions from distinct domains. In this work, we focus on a setting where domains share underlying structural patterns despite differences in their specific realizations. The task is particularly challenging in the absence of paired observations, which removes direct supervision across domains. We introduce a generative framework, called SerpentFlow (SharEd-structuRe decomPosition for gEnerative domaiN adapTation), for unpaired domain alignment. SerpentFlow decomposes data within a latent space into a shared component common to both domains and a domain-specific one. By isolating the shared structure and replacing the domain-specific component with stochastic noise, we construct synthetic training pairs between shared representations and target-domain samples, thereby enabling the use of conditional generative models that are traditionally restricted to paired settings. We apply this approach to super-resolution tasks, where the shared component naturally corresponds to low-frequency content while high-frequency details capture domain-specific variability. The cutoff frequency separating low- and high-frequency components is determined automatically using a classifier-based criterion, ensuring a data-driven and domain-adaptive decomposition. By generating pseudo-pairs that preserve low-frequency structures while injecting stochastic high-frequency realizations, we learn the conditional distribution of the target domain given the shared representation. We implement SerpentFlow using Flow Matching as the generative pipeline, although the framework is compatible with other conditional generative approaches. Experiments on synthetic images, physical process simulations, and a climate downscaling task demonstrate that the method effectively reconstructs high-frequency structures consistent with underlying low-frequency patterns, supporting shared-structure decomposition as an effective strategy for unpaired domain alignment.

翻译：域对齐泛指学习不同域之间数据分布的对应关系。本文研究一种特定场景：尽管各域的具体表现形式存在差异，但其底层结构模式是共享的。在缺乏配对观测数据的情况下，该任务尤其具有挑战性，因为这意味着跨域的直接监督不复存在。我们提出一种称为SerpentFlow（SharEd-structuRe decomPosition for gEnerative domaiN adapTation）的生成式框架，用于无配对域对齐。SerpentFlow在潜在空间中将数据分解为两个域共有的共享分量和域特定的分量。通过隔离共享结构并将域特定分量替换为随机噪声，我们构建了共享表示与目标域样本之间的合成训练配对，从而使得传统上仅限于配对场景的条件生成模型得以应用。我们将该方法应用于超分辨率任务，其中共享分量自然对应于低频内容，而高频细节则捕捉域特定的可变性。区分低频与高频分量的截止频率通过基于分类器的准则自动确定，从而确保数据驱动且域自适应的分解。通过生成保留低频结构并注入随机高频实现的伪配对，我们学习了给定共享表示条件下目标域的条件分布。我们采用流匹配（Flow Matching）作为生成管道实现SerpentFlow，尽管该框架也兼容其他条件生成方法。在合成图像、物理过程模拟和气候降尺度任务上的实验表明，该方法能有效重建与底层低频模式一致的高频结构，从而验证了共享结构分解作为无配对域对齐策略的有效性。