# Energy-oriented Diffusion Bridge for Image Restoration with Foundational Diffusion Models

arXiv: https://arxiv.org/abs/2604.10983 · HTML: https://mlsanity.com/paper/2604.10983/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 36 of its 47 references that are in the map.
- First posted on arXiv 13 Apr 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [MUSIQ: Multi-scale Image Quality Transformer](https://mlsanity.com/paper/2108.05997/) (2021)
- [Real-ESRGAN: Training Real-World Blind Super-Resolution with Pure Synthetic Data](https://mlsanity.com/paper/2107.10833/) (2021)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Deep Retinex Decomposition for Low-Light Enhancement](https://mlsanity.com/paper/1808.04560/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Simplifying, Stabilizing and Scaling Continuous-Time Consistency Models](https://mlsanity.com/paper/2410.11081/) (2024)
- [BBDM: Image-to-image Translation with Brownian Bridge Diffusion Models](https://mlsanity.com/paper/2205.07680/) (2022)
- [Attentive Generative Adversarial Network for Raindrop Removal from a Single Image](https://mlsanity.com/paper/1711.10098/) (2017)
- [Image Restoration with Mean-Reverting Stochastic Differential Equations](https://mlsanity.com/paper/2301.11699/) (2023)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [AdaIR: Adaptive All-in-One Image Restoration via Frequency Mining and Modulation](https://mlsanity.com/paper/2403.14614/) (2024)
- [Controlling Vision-Language Models for Multi-Task Image Restoration](https://mlsanity.com/paper/2310.01018/) (2023)
- [AutoDIR: Automatic All-in-One Image Restoration with Latent Diffusion](https://mlsanity.com/paper/2310.10123/) (2023)
- [Global Structure-Aware Diffusion Process for Low-Light Image Enhancement](https://mlsanity.com/paper/2310.17577/) (2023)
- [Selective Hourglass Mapping for Universal Image Restoration Based on Diffusion Model](https://mlsanity.com/paper/2403.11157/) (2024)
- [UniRestore: Unified Perceptual and Task-Oriented Image Restoration Model Using Diffusion Prior](https://mlsanity.com/paper/2501.13134/) (2025)
- [Image Restoration Through Generalized Ornstein-Uhlenbeck Bridge](https://mlsanity.com/paper/2312.10299/) (2023)
- [A Unified Conditional Framework for Diffusion-based Image Restoration](https://mlsanity.com/paper/2305.20049/) (2023)
- [UniDB: A Unified Diffusion Bridge Framework via Stochastic Optimal Control](https://mlsanity.com/paper/2502.05749/) (2025)

## Built on by (most cited first, 1 of 1)

- [PRISM: Principled Reference Identification for Schrodinger Bridge Model](https://mlsanity.com/paper/2608.06893/) (2026)

## Abstract (arXiv)

Diffusion bridge models have shown great promise in image restoration by explicitly connecting clean and degraded image distributions. However, they often rely on complex and high-cost trajectories, which limit both sampling efficiency and final restoration quality. To address this, we propose an Energy-oriented diffusion Bridge (E-Bridge) framework to approximate a set of low-cost manifold geodesic trajectories to boost the performance of the proposed method. We achieve this by designing a novel bridge process that evolves over a shorter time horizon and makes the reverse process start from an entropy-regularized point that mixes the degraded image and Gaussian noise, which theoretically reduces the required trajectory energy. To solve this process efficiently, we draw inspiration from consistency models to learn a single-step mapping function, optimized via a continuous-time consistency objective tailored for our trajectory, so as to analytically map any state on the trajectory to the target image. Notably, the trajectory length in our framework becomes a tunable task-adaptive knob, allowing the model to adaptively balance information preservation against generative power for tasks of varying degradation, such as denoising versus super-resolution. Extensive experiments demonstrate that our E-Bridge achieves state-of-the-art performance across various image restoration tasks while enabling high-quality recovery with a single or fewer sampling steps. Our project page is https://jinnh.github.io/E-Bridge/.