UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control

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UniDB

Here we briefly compare the performance of UniDB to diffusion bridge with Doob's h-transform across various tasks, including Super-resolution, Inpainting and Deraining. UniDB effectively balances control and terminal costs by modifying the terminal penalty coefficient, alleviating the problems caused by Doob's h-transform in these applications. This framework significantly boosts the detail rendering ability of generated images while imposing minimal overhead in code modifications.

Abstract

Recent advances in diffusion bridge models leverage Doob’s h-transform to establish fixed endpoints between distributions, demonstrating promising results in image translation and restoration tasks. However, these approaches frequently produce blurred or excessively smoothed image details and lack a comprehensive theoretical foundation to explain these shortcomings. To address these limitations, we propose UniDB, a unified framework for diffusion bridges based on Stochastic Optimal Control (SOC). UniDB formulates the problem through an SOC-based optimization and derives a closed-form solution for the optimal controller, thereby unifying and generalizing existing diffusion bridge models. We demonstrate that existing diffusion bridges employing Doob’s h-transform constitute a special case of our framework, emerging when the terminal penalty coefficient in the SOC cost function tends to infinity. By incorporating a tunable terminal penalty coefficient, UniDB achieves an optimal balance between control costs and terminal penalties, substantially improving detail preservation and output quality. Notably, UniDB seamlessly integrates with existing diffusion bridge models, requiring only minimal code modifications. Extensive experiments across diverse image restoration tasks validate the superiority and adaptability of the proposed framework. Our code is available at https://github.com/UniDB-SOC/UniDB/

UniDB

We provide the relevant simple-version pseudo-code for our UniDB-GOU model as an example regarding the training and sampling process. The two algorithms encapsulate the core methodologies employed by our model to learn and explain how to restore HQ images from LQ images. Also, the red and the green parts highlight the main difference between UniDB and GOUB.

PPT

BibTeX

@misc{zhu2025unidbunifieddiffusionbridge,
        title={UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control}, 
        author={Kaizhen Zhu and Mokai Pan and Yuexin Ma and Yanwei Fu and Jingyi Yu and Jingya Wang and Ye Shi},
        year={2025},
        eprint={2502.05749},
        archivePrefix={arXiv},
        primaryClass={cs.CV},
        url={https://arxiv.org/abs/2502.05749}, 
  }