# Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge

arXiv: https://arxiv.org/abs/2305.15086 · HTML: https://mlsanity.com/paper/2305.15086/

## Key facts

- Cited by 96 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 44 of its 57 references that are in the map.
- First posted on arXiv 24 May 2023.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 44)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theory](https://mlsanity.com/paper/2110.11291/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Path Integral Sampler: a stochastic control approach for sampling](https://mlsanity.com/paper/2111.15141/) (2021)
- [EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations](https://mlsanity.com/paper/2207.06635/) (2022)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Diffusion Schr"odinger Bridge Matching](https://mlsanity.com/paper/2303.16852/) (2023)
- [Solving Schr"odinger Bridges via Maximum Likelihood](https://mlsanity.com/paper/2106.02081/) (2021)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Geometry-Consistent Generative Adversarial Networks for One-Sided Unsupervised Domain Mapping](https://mlsanity.com/paper/1809.05852/) (2018)
- [Deep Generative Learning via Schr"odinger Bridge](https://mlsanity.com/paper/2106.10410/) (2021)

## Built on by (most cited first, 30 of 96)

- [Light and Optimal Schr"odinger Bridge Matching](https://mlsanity.com/paper/2402.03207/) (2024)
- [Self-Consistent Recursive Diffusion Bridge for Medical Image Translation](https://mlsanity.com/paper/2405.06789/) (2024)
- [IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Models](https://mlsanity.com/paper/2311.06792/) (2023)
- [Discrete Diffusion Schr"odinger Bridge Matching for Graph Transformation](https://mlsanity.com/paper/2410.01500/) (2024)
- [Fr'echet Radiomic Distance (FRD): A Versatile Metric for Comparing Medical Imaging Datasets](https://mlsanity.com/paper/2412.01496/) (2024)
- [Light Schr"odinger Bridge](https://mlsanity.com/paper/2310.01174/) (2023)
- [DiffV2IR: Visible-to-Infrared Diffusion Model via Vision-Language Understanding](https://mlsanity.com/paper/2503.19012/) (2025)
- [Implicit Image-to-Image Schrodinger Bridge for Image Restoration](https://mlsanity.com/paper/2403.06069/) (2024)
- [Adversarial Schr"odinger Bridge Matching](https://mlsanity.com/paper/2405.14449/) (2024)
- [CUNSB-RFIE: Context-aware Unpaired Neural Schr"odinger Bridge in Retinal Fundus Image Enhancement](https://mlsanity.com/paper/2409.10966/) (2024)
- [StainDiffuser: MultiTask Dual Diffusion Model for Virtual Staining](https://mlsanity.com/paper/2403.11340/) (2024)
- [Generalized Consistency Trajectory Models for Image Manipulation](https://mlsanity.com/paper/2403.12510/) (2024)
- [Neural Schr"odinger Bridge with Sinkhorn Losses: Application to Data-driven Minimum Effort Control of Colloidal Self-assembly](https://mlsanity.com/paper/2307.14442/) (2023)
- [Distribution Prototype Diffusion Learning for Open-set Supervised Anomaly Detection](https://mlsanity.com/paper/2502.20981/) (2025)
- [Towards Robust Event-based Networks for Nighttime via Unpaired Day-to-Night Event Translation](https://mlsanity.com/paper/2407.10703/) (2024)
- [Bidirectional Diffusion Bridge Models](https://mlsanity.com/paper/2502.09655/) (2025)
- [When Schr"odinger Bridge Meets Real-World Image Dehazing with Unpaired Training](https://mlsanity.com/paper/2507.09524/) (2025)
- [F2FLDM: Latent Diffusion Models with Histopathology Pre-Trained Embeddings for Unpaired Frozen Section to FFPE Translation](https://mlsanity.com/paper/2404.12650/) (2024)
- [MixBridge: Heterogeneous Image-to-Image Backdoor Attack through Mixture of Schr"odinger Bridges](https://mlsanity.com/paper/2505.08809/) (2025)
- [Synthetic to Authentic: Transferring Realism to 3D Face Renderings for Boosting Face Recognition](https://mlsanity.com/paper/2407.07627/) (2024)
- [Scalable Simulation-free Entropic Unbalanced Optimal Transport](https://mlsanity.com/paper/2410.02656/) (2024)
- [Paired Wasserstein Autoencoders for Conditional Sampling](https://mlsanity.com/paper/2412.07586/) (2024)
- [Deterministic Image-to-Image Translation via Denoising Brownian Bridge Models with Dual Approximators](https://mlsanity.com/paper/2512.23463/) (2025)
- [Rethinking Perceptual Metrics for Medical Image Translation](https://mlsanity.com/paper/2404.07318/) (2024)
- [Single-Step Bidirectional Unpaired Image Translation Using Implicit Bridge Consistency Distillation](https://mlsanity.com/paper/2503.15056/) (2025)
- [System-Embedded Diffusion Bridge Models](https://mlsanity.com/paper/2506.23726/) (2025)
- [TherA: Thermal-Aware Visual-Language Prompting for Controllable RGB-to-Thermal Infrared Translation](https://mlsanity.com/paper/2602.19430/) (2026)
- [OCT2Confocal: 3D CycleGAN based Translation of Retinal OCT Images to Confocal Microscopy](https://mlsanity.com/paper/2311.10902/) (2023)
- [MRGen: Segmentation Data Engine for Underrepresented MRI Modalities](https://mlsanity.com/paper/2412.04106/) (2024)
- [Universal Vessel Segmentation for Multi-Modality Retinal Images](https://mlsanity.com/paper/2502.06987/) (2025)

## Abstract (arXiv)

Diffusion models are a powerful class of generative models which simulate stochastic differential equations (SDEs) to generate data from noise. While diffusion models have achieved remarkable progress, they have limitations in unpaired image-to-image (I2I) translation tasks due to the Gaussian prior assumption. Schr"odinger Bridge (SB), which learns an SDE to translate between two arbitrary distributions, have risen as an attractive solution to this problem. Yet, to our best knowledge, none of SB models so far have been successful at unpaired translation between high-resolution images. In this work, we propose Unpaired Neural Schr"odinger Bridge (UNSB), which expresses the SB problem as a sequence of adversarial learning problems. This allows us to incorporate advanced discriminators and regularization to learn a SB between unpaired data. We show that UNSB is scalable and successfully solves various unpaired I2I translation tasks. Code: urlhttps://github.com/cyclomon/UNSB