# UniCycleFlow: Bidirectional Unpaired Image Translation with a Shared Rectified Flow

arXiv: https://arxiv.org/abs/2608.06784 · HTML: https://mlsanity.com/paper/2608.06784/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 19 of 19)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [DualGAN: Unsupervised Dual Learning for Image-to-Image Translation](https://mlsanity.com/paper/1704.02510/) (2017)
- [Geometry-Consistent Generative Adversarial Networks for One-Sided Unsupervised Domain Mapping](https://mlsanity.com/paper/1809.05852/) (2018)
- [Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge](https://mlsanity.com/paper/2305.15086/) (2023)
- [The Spatially-Correlative Loss for Various Image Translation Tasks](https://mlsanity.com/paper/2104.00854/) (2021)
- [Dual Contrastive Learning for Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/2104.07689/) (2021)
- [One-to-one Mapping for Unpaired Image-to-image Translation](https://mlsanity.com/paper/1909.04110/) (2019)

## Abstract (arXiv)

Bidirectional unpaired image translation must preserve source-specific structure while learning coherent transformations in both directions without paired supervision. Existing methods typically employ two direction-specific generators or train separate one-way models. Even when linked by cycle consistency, such models constrain only the round-trip endpoint reconstruction, without requiring the two directions to obey a common local transformation rule. We propose UniCycleFlow, a rectified-flow framework that represents bidirectional translation as forward and reverse integration of a single time-conditioned velocity field. This formulation organizes both directions within the same continuous dynamics, rather than coupling otherwise separate endpoint mappings. A key challenge is that unpaired data provide no meaningful source--target coupling from which rectified-flow trajectories can be constructed. UniCycleFlow addresses this challenge by learning deterministic source-conditioned endpoints whose marginal distributions are adversarially matched to the opposite domains. The resulting paths are regularized by stop-gradient self-flow matching for intermediate velocity supervision, discrete cycle closure for forward--reverse consistency, and representation path-velocity regularization for controlling localized feature changes along the trajectory. Across ten translation directions, UniCycleFlow achieves the lowest FID on 7 of 10 tasks using a single Euler evaluation and obtains the best average FID of 55.1.