# SerpentFlow: Generative Unpaired Domain Alignment via Shared-Structure Decomposition

arXiv: https://arxiv.org/abs/2601.01979 · HTML: https://mlsanity.com/paper/2601.01979/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 5 Jan 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Unsupervised Image Super-Resolution using Cycle-in-Cycle Generative Adversarial Networks](https://mlsanity.com/paper/1809.00437/) (2018)
- [A Fourier Space Perspective on Diffusion Models](https://mlsanity.com/paper/2505.11278/) (2025)
- [Schr"odinger Bridge Flow for Unpaired Data Translation](https://mlsanity.com/paper/2409.09347/) (2024)
- [AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows](https://mlsanity.com/paper/1905.12892/) (2019)
- [ClimAlign: Unsupervised statistical downscaling of climate variables via normalizing flows](https://mlsanity.com/paper/2008.04679/) (2020)
- [Unpaired Downscaling of Fluid Flows with Diffusion Bridges](https://mlsanity.com/paper/2305.01822/) (2023)
- [Don't Start from Scratch: Behavioral Refinement via Interpolant-based Policy Diffusion](https://mlsanity.com/paper/2402.16075/) (2024)
- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [Physics-informed kernel learning](https://mlsanity.com/paper/2409.13786/) (2024)

## Built on by (most cited first, 4 of 4)

- [Super-Resolving Coarse-Resolution Weather Forecasts With Flow Matching](https://mlsanity.com/paper/2604.00897/) (2026)
- [Generative Unsupervised Downscaling of Climate Models via Domain Alignment: Application to Wind Fields](https://mlsanity.com/paper/2604.03341/) (2026)
- [RainAtlas: A Multi-Continental Dataset for Precipitation Downscaling](https://mlsanity.com/paper/2609.39833/) (2026)
- [Unsupervised Domain Adaptation for Enhanced Radiometer Image Precipitation Estimation using Conditional Flow Matching](https://mlsanity.com/paper/2610.01890/) (2026)

## Abstract (arXiv)

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.