SerpentFlow: Generative Unpaired Domain Alignment via Shared-Structure Decomposition

TL;DR

SerpentFlow introduces a principled, unpaired-domain-alignment approach that explicitly decomposes data into shared and domain-specific components and uses stochastic high-frequency content to generate pseudo-pairs for conditional generation. A frequency-based instantiation in the Fourier domain with an automatically learned cutoff ensures the shared backbone captures domain-invariant structure while domain-specific details are synthesized, enabling effective unsupervised super-resolution via Flow Matching. Across synthetic images, fluid simulations, and climate downscaling, SerpentFlow consistently preserves low-frequency content and reconstructs plausible high-frequency details, outperforming state-of-the-art unpaired methods in fidelity and statistical consistency. The framework is general, data-driven, and adaptable to temporal or spatio-temporal domains, offering a robust pathway for unpaired domain alignment in diverse scientific and engineering applications.

Abstract

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.

Figures (21)

• Figure 1: MRBI Reconstruction Comparison, for an image labeled 8, with $w_c=4$.
• Figure 2: Effect of stochastic high-frequency components in MRBI reconstruction. Top row: optimal configuration (model trained with $w_c=4$, inference done with $w_c=4$), bottom row: training with stronger low-frequency filtering: $w_c=3$, but inference done with $w_c=4$. Left: generated images, including multiple noisy predictions and one without noise. Right: corresponding deviations from the ground truth.
• Figure 3: Vorticity and supersaturation fields at a given iteration for $\mathcal{D}_{B_8}$, $\mathop{\mathrm{\mathcal{D}_A}}\nolimits$, and reconstructions from the baselines.
• Figure 4: Spatially averaged temporal evolution of low- and high-resolution fields for $k_x=k_y=8$.
• Figure 5: Density and spectral density comparisons for low- and high-resolution fields and baselines ($k_x=k_y=8$).

Theorems & Definitions (3)

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