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

Jinhui Hou; Zhiyu Zhu; Junhui Hou

cs.CVApr 13, 2026

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

Authors: Jinhui Hou, Zhiyu Zhu, Junhui Hou

Organizations: Department of Computer Science, City University of Hong Kong · Department of Computer Science, City University of Hong Kong (Dongguan)

Abstract

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/.

Figures & tables

Figure 1: Illustration of diffusion processes for image restoration. (a) Standard Diffusion Models: These traverse a long, high-energy trajectory starting from pure Gaussian noise to the clean image manifold, conditioned on the degraded image. (b) Conventional Bridge Models: These construct a path from the degraded to the clean image but often follow a sub-optimal, high-energy trajectory that includes a redundant ”re-noising” phase before denoising. (c) Our E-Bridge: It starts the reverse process from an entropy-regularized point, which is a mixture of the degraded image and noise, thus bypassing the inefficient re-noising phase and creating a more direct and shorter path for restoration.

Task	Method	NFE $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$	FID $\downarrow$	NIQE $\downarrow$	MUSIQ $\uparrow$
	DiffBIR ( Lin et al., 2024 )	50	22.601	0.404	77.767	4.333	64.767
	AutoDIR ( Jiang et al., 2024 )	25	23.953	0.419	64.995	5.599	48.103
	UniDB † ( Zhu et al., 2025a )	100	20.778	0.477	87.135	3.882	62.004
	IRBridge † ( Wang et al., 2025a )	100	23.615	0.415	59.539	5.215	65.535
	MaRS † ( Li et al., 2025 )	20	23.325	0.525	104.665	6.328	53.162
	MaRS † ( Li et al., 2025 )	10	23.786	0.539	101.978	7.251	49.489

Table 1: Quantitative comparisons of different diffusion-based methods across multiple image restoration tasks. The best results are highlighted in bold .

{\dagger}

represents that we utilized the official public code and recommended settings to train the baseline on the same training dataset as ours.

Figure 2: Visual comparison of different methods across various tasks.

Task	NFE	(a)				(b)				Ours
Task	NFE	PSNR $\uparrow$	LPIPS $\downarrow$	MUSIQ $\uparrow$	NIQE $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$	MUSIQ $\uparrow$	NIQE $\downarrow$	PSNR $\uparrow$	LPIPS $\downarrow$	MUSIQ $\uparrow$	NIQE $\downarrow$
Super-resolution	10	20.527	0.464	63.476	3.973	19.945	0.446	69.157	4.958	21.282	0.346	70.868	3.839
	5	21.016	0.495	56.709	5.657	21.443	0.502	63.068	3.902	22.477	0.356	65.342	4.373
	1	19.667	0.486	31.919	7.166	22.039	0.481	35.552	4.267	24.094	0.452	44.605	6.251
Denoising	10	24.241	0.288	64.724	4.952	24.391	0.261	69.976	5.575	26.069	0.184	69.736	3.514
	5	23.701	0.316	60.090	5.235	25.279	0.235	65.870	3.807	26.649	0.182	67.507	4.492

Table 2: Ablation study on the impact of the proposed geodesic trajectory. Specifically, we replaced the geodesic trajectory with two other types of trajectories, i.e., a ) the standard diffusion trajectory, starting from pure Gaussian noise to the clean image manifold, and b ) the conventional bridge trajectory, which constructs a trajectory from the degraded to the clean image, often follows a ”re-noising” phase before denoising. Best results in each row are in bold .

Method	NFE	Denoising				Super-res.				Raindrop rem.				Low-light Enh.				Demoireing
Method	NFE	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$
DDIM	50	26.31	0.176	69.01	3.55	21.73	0.330	69.37	3.26	29.20	0.090	68.81	3.14	25.37	0.112	71.48	4.08	20.15	0.221	62.80	5.15
	20	26.53	0.185	68.79	3.94	21.99	0.353	68.85	3.86	29.51	0.086	67.10	3.27	25.45	0.112	70.83	4.19	20.31	0.303	62.35	5.31
	10	26.71	0.195	67.44	4.58	22.27	0.362	67.17	5.02	29.72	0.086	66.46	3.57	25.57	0.111	70.61	4.32	20.43	0.327	62.02	5.50
	1	24.56	0.270	57.07	4.30	17.92	0.591	46.07	8.97	27.48	0.135	62.42	4.39	20.96	0.177	63.78	4.27	17.44	0.407	44.21	5.33
Ours	10	26.06	0.184	69.74	3.51	21.28	0.346	70.87	3.84	29.22	0.079	70.01	3.22	25.54	0.097	71.68	4.20	20.26	0.313	63.93	5.22

Table 3: Comprehensive efficiency comparison between our consistency-based solver (E-Bridge) and a traditional iterative ODE solver (DDIM). (P: PSNR

\uparrow

, L: LPIPS

\downarrow

, M: MUSIQ

\uparrow

, N: NIQE

\downarrow

). Best results in each column are in bold .

Task	$T_{0}=0.3$				$T_{0}=0.5$				$T_{0}=0.7$				$T_{0}=0.9$
Task	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$	P $\uparrow$	L $\downarrow$	M $\uparrow$	N $\downarrow$
Super-resolution	21.12	0.457	62.16	4.88	21.49	0.397	67.00	4.36	21.82	0.359	68.77	3.84	21.28	0.346	70.87	3.84
Denoising	24.43	0.276	66.13	4.48	25.35	0.206	69.24	3.74	26.06	0.184	69.73	3.51	26.53	0.185	69.13	4.04
Low-light	24.89	0.129	68.55	3.91	25.12	0.118	70.93	4.07	25.35	0.107	71.39	4.15	25.54	0.097	71.68	4.20
Raindrop removal	29.61	0.080	67.38	3.45	29.74	0.081	66.73	3.57	29.70	0.083	65.23	3.821	29.21	0.092	63.98	3.97
Demoiréing	20.85	0.234	61.67	5.34	20.85	0.230	62.16	5.44	19.76	0.249	61.32	5.60	16.47	0.328	59.04	5.68

Table 4: Analysis of the trajectory horizon parameter

T_{0}

. (P: PSNR

\uparrow

, L: LPIPS

\downarrow

, M: MUSIQ

\uparrow

, N: NIQE

\downarrow

). Best results for each task are in bold .

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Method	Training Parameters	Inference Time per Step	NFE	Total Inference Time
AutoDIR	115.9 M	0.823s	25	20.58s
UniDB	137.1 M	1.243s	100	124.30s
IRBridge	361.3 M	0.263s	100	26.30s
UniDB++	137.1 M	1.224s	10	12.24s
Ours	743.8 M	0.673s	10	6.73s

Appendix

Table F-5: Computational efficiency comparison on the

1024\times 1024

image denoising.

Figure F-3: Additional visual results on image super-resolution in the wild.

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