UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control
This work addresses the problem of image detail preservation in diffusion bridge models for computer vision researchers and practitioners, providing an incremental yet significant improvement over existing approaches.
The authors tackled the problem of diffusion bridge models producing blurred image details and established a unified framework, UniDB, which achieves an optimal balance between control costs and terminal penalties, resulting in substantially improved detail preservation and output quality. UniDB generalizes existing diffusion bridge models and requires minimal code modifications to integrate with them.
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/.