UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control

TL;DR

UniDB introduces a unified diffusion bridge framework based on Stochastic Optimal Control that improves image restoration quality by balancing control costs and terminal penalties, unifying existing models and enhancing detail preservation.

Contribution

It formulates diffusion bridges through SOC, derives a closed-form optimal controller, and unifies existing models as special cases, enabling better image restoration results.

Findings

Outperforms existing diffusion bridge models in image restoration tasks.

Unifies various diffusion bridge approaches under a single SOC-based framework.

Requires minimal code changes to integrate with existing models.

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/.