Degradation-Aware Dynamic Schrödinger Bridge for Unpaired Image Restoration
Authors: Jingjun Yi
Qi Bi
Hao Zheng
Huimin Huang
Yixian Shen
Haolan Zhan
Wei Ji
Yawen Huang
Yuexiang Li
Xian Wu
Yefeng Zheng
Venue: NeurIPS 2025 poster ()
Keywords: Unpaired Image Restoration
Schrödinger Bridge
Optimal Transport
Primary area: deep_learning
TL;DR: This paper addresses the fundamental problem of Unpaired Image Restoration through a principled formulation based on the Optimal Transport dynamics of Schrödinger Bridge.

Abstract: Image restoration is a fundamental task in computer vision and machine learning, which learns a mapping between the clear images and the degraded images under various conditions (e.g., blur, low-light, haze).
Yet, most existing image restoration methods are highly restricted by the requirement of degraded and clear image pairs, which limits the generalization and feasibility to enormous real-world scenarios without paired images.
To address this bottleneck, we propose a Degradation-aware Dynamic Schr\"{o}dinger Bridge (DDSB) for unpaired image restoration.
Its general idea is to learn a Schr\"{o}dinger Bridge between clear and degraded image distribution, 
while at the same time emphasizing the physical degradation priors to reduce the accumulation of errors during the restoration process. 
A Degradation-aware Optimal Transport (DOT) learning scheme is accordingly devised.
Training a degradation model to learn the inverse restoration process is particularly challenging, as it must be applicable across different stages of the iterative restoration process.
A Dynamic Transport with Consistency (DTC) learning objective is further proposed to reduce the loss of image details in the early iterations and therefore refine the degradation model.
Extensive experiments on multiple image degradation tasks show its state-of-the-art performance over the prior arts.

Degradation-aware Dynamic Schrödinger Bridge for Unpaired Image Restoration
Jingjun 2 Qi Bi Bi
Hao Zheng 4b4 Huimin Huang', Yixian Shen', Haolan Zhan", Wei Ji Yawen Huang', Yuexiang Li", Xian Wu Yefeng Zheng DX
Westlake University, China, PUniversity of Alberta, Canada University of Amsterdam, the Netherland, *eeneett Jarvis Lab, China Monash University, Australia, Yale University, the United States, 'University of Macau, Macau q b.@iiieee..rg org, howzheng@tencent. com, zhengyefengdvestlake edu.
Abstract
Image restoration a fundamental task in computer vision and machine learning, which learns mapping between the clear images and the degraded images under various conditions (c.g.. blur, low-light, haze). Yet, most existing image restoration methods are highly restricted by the requirement of degraded and clear image pairs, which limits the generalization and feasibility to enormous real-world scenarios without paired images. To address this bottleneck, Dynamic Schrödinger Bridge (DDSB) for unpaired image restoration. Its general idea is to learn Schrödinger Bridge between clear and degraded image distribution, while at the same time emphasizing the physical degradation priors to reduce the ac- cumulation of errors during the restoration process. A Degradation-aware Optimal Transport (DOT) learning scheme is accordingly devised. Training a degradation model learn the inverse restoration process is particularly challenging, it must be applicable across different stages of the iterative restoration process. A Dynamic Transport with Consistency (DTC) learning objective is further proposed to reduce the loss of image details in the early iterations and therefore refine the degradation model. Extensive experiments on multiple image degradation tasks show its state-of-the-arr performance over the prior arts.
propose Degradation-awy awwaee
Introduction
Image restoration, encompassing tasks like denoising, deblurring, and dehazing, one of the most crucial yet fundamental challenges in computer vision B
[8 54] A traditional paradigm is supervised learning, where paired data clear and degraded images are used to train models. However, acquiring large-scale paired datasets in many real-world scenarios is often impractical due to the vast diversity of degradation conditions and the absence of ground truth. Unpaired image restoration methods, which learn mappings between unpaired degraded and clear image sets, have gained significant
attention in recent years as an alternative solution [30 (8,55) (47). However, one of its key challenges lies in the absence of explicit correspondences between the input and output images.
The realm of generative models, exemplified by the recent diffusion models 38
has achieved remarkable progress over the past few years. Compared with the prior arts (e.g., generative adversarial networks [14), variational autoencoders [23]). these recent generative models are more capable to generate diverse and high-quality samples [50], and have shown great success in image restoration 77]. Unfortunately, diffusion models are still subject to specific prior distribution, e.g., Gaussian, which prevents its full potential various degradation conditions in image restoration.
"innjun is affiliated with University of Alberta. This rescarch was conducted when he was a research intern at Westlake University.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Dellane
Dotain
Rairdrop
Deftaindrp
Dj1
Debliar
Degradation Sample
Static Trnnport
Lowilght
D4
Relight
Clean
Dyramic
D pan
Sample
Transpott
Ckem
Degradation Images
Dynamic Schrödinger Bridge
Clean Images
Figure 1: Dynamic Schrödinger bridge formulates image restoration as an optimal transport between the clear and degraded images, while maintaining the flexibility to handle unpaired data.
Schrödinger bridge (SB) provides promising alternative by formulating the restoration problem as an optimal transport (OT) task between clear image distribution and the degraded image distribution, while maintaining the flexibility to handle unpaired data [9 6 43 In contrast to prior generative models, enables the translation between two arbitrary distributions without requiring
paired training data 45 29 10
39 5].
In light of these properties, the first research question naturally arises: How to leverage SB for umpaired image restoration, while achieve as physically meaningful and realistic restoration as possible? To address this challenge, we propose Degradation -awaattioo--wrreeeee aware Optimal Transport (DOT) learning scheme, which builds the entropy- regulaigre OT framework inherent in SB. The core objective of DOT is reduce the accumulation of errors from unpaired SB during the iterative restoration process. By introducing a degradation model to learn the inverse process of restoration, DOT can amplify the degradations and artifacts produced by the restoration model, and impose an additional constraint based this information.
Training the degradation model particularly challenging due to the absence of paired training data, and this difficulty is compounded by the need for the model to generalize across different stages of the iterative restoration process. In the early stages iteration, the predicted clean images often contain excessive artifacts, whereas in the later stages, the differences between consecutive steps become minimal. Both scenarios are suboptimal for effective degradation model training. address these issues, we introduce Dynamic Transport with Consistency (DTC), which not only strengthens the constraints on the early stages, thereby reducing the loss of image details, but also refines the learning objective of the degradation model. This dual approach alleviates the challenges associated with learning the inverse restoration process and improves the overall effectiveness of the model.
Both components are incorporated as the proposed Degradation-aware Dynamic Schrödinger Bridge (DDSB). ensures that the restoration process remains robust to variations the degradation types, while preserving the integrity of the underlying image structure. The effectiveness of our method is validated through extensive experiments on multiple image restoration tasks, including denoising, deblurring, and dehazing, across range of degradation conditions, in terms of both visual quality and quantitative metrics. particular, our approach demonstrates superior generalization to unseen degradation types, providing more robust solution for real-world image restoration tasks.
In nutshell, our contributions can be summarized follows.
This paper opens up a new direction for applying Schrödinger Bridge in unpaired image restoration, providing promising solution to the limitations of existing techniques.
A Degradation-aware Dynamic Schrödinger Bridge (DDSB) is developed for unpaired image restoration, which incorporates degradation model reduce the error accumulation during the transport process.

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A Dynamic Transport with Consisteney (DTC) learning objective is proposed to optimize the training of the degradation model.
Extensive experiments multiple image restoration benchmarks show its state-of-the-art performance.
2
Related Works
Schrödinger Bridge (SB) problem, also known as rngropy-regularizze optimal transport B7 24),
aims leam stochastic process between initial distribution and specified terminal distribution over time under the guidance of a reference measure. Owing to its property to allow arbitrary choices of initial and terminal distributions, SB has fostered the development of variety of generative modeling problems, to name a few, iterative proportional fitting (9 44). Riemannian manifolds (42,
image translation [41], path sampling [55] 36]. unpaired transport 222] under both supervised settings [I5 29 I0 and unsupervised settings 455 In contrast to earlier work [49], the proposed method innovatively integrates dynamic multi-step transport modeling and trajectory consistency regularization. Besides, it is capable to handle various degradation types over deraining in 49
Unpaired Image-to-Image (I2I) Translation aims to generate target image that preserves the structural similarity of the source image without wair-wise input [59] 19]. Early works usually leverage geometric consistency [12] and mutual information regularization []. More recently, contrastive have advanced 121 tasks by refining
unpaired translation (CUT) and its variants [32 21
46 57
patch-wise regularization. Santa [51] introduces shortest-path constraints, while DN (18] applies dense normalization for translation. However, recent works usually conduct unpaired 121 under resolution higher than 128 128 pixels. In contrast, under our image restoration task, 12I requires substantially higher resolutions, which poses significant challenges. In addition, the proposed method conceptually distinct from the previous circle consistency learning objective (e.g., CycleGAN (59) by further imposing adaptive constraint on the SB path to align with plausible degradation outcomes and introducing temporal consistency across intermediate SB steps.
Unpaired Image Restoration aims to recover clean images from degraded ones without requiring aligned supervision (58). Classical priors like DCP [16] rely on statistical assumptions, while recent domain-specific approaches, like YOLY [26] and USID-Net [27). exploit layer disentanglemen
and uncertainty-awwat representations. CycleGAN (59 pioneered the use of cycle-consistency loss, while later works incorporated depth-aware degradation modeling
[53] 56). mutal information
maximization [32], and degradation feature decoupling
[47]. However, the reliance on adversarial
losses or handcrafted constraints makes it difficult to enforce degradation consistency throughout the restoration forward trajectory. In contrast, our method opens a new direction by introducing Schrödinger bridge to unpaired restoration.
Preliminaries
Schrödinger Bridge. Given two probability distributions To and T over RR, the Schrödinger Bridge problem seeks the most likely stochastic trajectory (athtej.,)) that evolves from To to Ti. Let I2 denote the space of continuous paths in Rd,, and let PS2)) represent the collection of path measures. The SB problem can be formulated as the following entropy- regula-erggllriize variational problem:
arg min KL(Q) WT) s.t. Qo
Q T1
CEP(O)
where W is the Wiener measure with diffusion parameter r, and Q. represents the marginal at time The solution Q' defines the Schrödinger Bridge connecting mo to T
Two perspective--soochee problem and guide our model design. Both are central to understanding the shortcomings prior SB methods and motivating our approach.
control and static coupling-off foundational insight into the SB
Stochastic Control Formulation. From the viewpoint of stochastic control 333. the SB process {o,} ~ Q* satisfies a stochastic differential equation dx, = u, dt /ddw,, where u, is the optimal control minimizing the expected energy of the drift:
dx; u + /Tdw,
u arg min E
|n 2dt
s.t.
Fa To. C. ~ TT.
3

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Xiraj
Kd - /=
X j11
@o (x
time idx
DTC
NCO,
(ni)
1+
Py+1
D
2
update
iteraion
X Xx
DOT
4o (x
Adv
Degradation-ANe Aware Optimal Transport
Dynamic Transport with Consistency
(x.)
([De(tt) xtll
Degrabition Modal
Conva333
Cost Piane
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Transport Cost
Conza333
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Figure 2: Framework overview of the proposed Degradation-awer aware Dynamic Schrödinger Bridge (DDSB). On top of the unpaired Schrödinger Bridge model, it presents two novel components, namely, Degradation-awar Optimal Transport (DOT) and Dynamic Transport with Consistency (DTC).
This formulation reveals that SB paths minimum-actioo acttio stochastic processes constrained to match boundary distributions. The resulting trajectory is both Markovian and converges to the deterministic optimal transport flow as
O, with determining the stochasticity level.
Static Coupling. SB also admits a static formulation based on endpoint marginals. If the joint known, denoted Qh then intermediate states are conditionally Gaussian, given by p(a: Ma, 2:2) Nax,, (1 t)aaa + tat,, rf(1 t)T). This allows trajectory simulation by sampling from the coupling Q6 and the marginal density of given æa is thus:
distribution at times f = 0 and
p(a; wa) = p(ac. æa x.) dQijola x.a).
The optimal coupling Qn satisfies the entropy-regularized optimal transport (EROT) formulation:
Qii arg min E(ee.a)) [||ær x. 1 2TH((7),
=EI1(x..81)
where [[(TO, mi) denotes the set of couplings with marginals and æı and H(7) is the entropy.
4 Method
unpaired image restoration, the source and target distributions represent degraded and clean visual domains, respectively. While Schrödinger Bridge (SB) offers principled probabilistic framework to interpolate between two distributions via entropy-regularized optimal transport (EROT), conventional formulations often neglect physical degradation priors that are crucial for realism in restoration tasks. We propose a novel formulation Degradation-aved explicitly integrates differentiable degradation model within the SB formulation. DDSB enforces that the restored outputs remain consistent with their degraded inputs under learned degradation dynamics. The framework overview is shown in Fig. 2
Dynamic Schrödinger Bridge (DDSB) that
4.1 Unpaired Schrödinger Bridge (UNSB)
The DDSB framework formulates the Schrödinger Bridge as composition of learnable generative transitions that iteratively transport samples from degraded distribution toward the clean image

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denote real degraded image, where Fu is the degraded image distribution. The objective is recover its corresponding clean counterpart 3, Te. with n. representing the clean image distribution. Consider discretized time partition {4: of the unit interval [0, 1], where ln = 0, IN = 1, and 1, < 11+1- The UNSB process can be simulated via a Markov chain:
distribution. Let
p(( }) p( [= .. p( ((
(5)
Here, Eto corresponds to the degraded input æa, while Fyy approximates the clean image To approximate p(at;); ). a conditional generator qo, (2rgla),) ) is introduced, where 02 denotes the network
parameters at step i. This defines joint distribution between the latent state and the clean target as:
qo, ( Øe) qo, (ate (erk,,)))i (((,),
(xe) = (Ep(..,) (at, (2t))
(6)
Given sample 2t, go (zt;)) the generator predicts clean estimate (x( (o(2)((11)) A new sample 2ty is then obtained by interpolating Di, with xe (xt,) and injecting noise:
p( Lt,) = =N (Ziees My+1 + (1 o
(7)
where Mj+1 1341 controls the interpolation weight, and the noise scale is computed 0 1-1,
115+((1 - (1)1) -1 t2). with r being a hyperparameter.
By iteratively applying this transition for j 0, 1......-11.. sample 2t, is generated. When the generator Qo. is sufficiently optimized, its marginal qu, (2r,,) closely approximates the target p(ar.). The sequence (x,,,) thus forms a progressively refined trajectory toward clean image reconstruction. The optimal parameters 0 are obtained by optimizing the Schrödinger Bridge via entropy-rcgularize optimal transport (EROT), defined as
LEROT an |||1 I.ll 2T H(T) + (L(go( p(are)), II(TT, Te).
(8)
Specifically, the first term of LEROT seeks stochastic coupling x² between Ta and me:
π². arg min B( [||a x.l? =Ell(xa.me))
[ - 2T H(T,,
where H((T) is the joint entropy and T a temperature hyperparameter. measures the reconstruction error between the predicted clean sample and the clean targe.
To ensure that the clean images inferred from qo (ar,) match the target distribution p(æ.), the second term uses an adversarial Kullback-Leibler (KL) regularization, given by:
Ladv = (L(go(x))) || p(x:.))
(10)
which enforces marginal alignment at the clean endpoint. This loss acts as global guidance signal complementing local transport fidelity, encouraging the generator to produce clean estimates that are statistically indistinguishable from real data. In practice, this term implemented via a discriminator network and optimized using reverse KL objective.
4.2 Degradation- Optimal Transport
To enhance the Schrödinger Bridge optimization in unpaired restoration, we introduce Degradation- aware Optimal Transport (DOT), which integrates degradation consistency into the EROT framework. An important issue with the aforementioned SB process is the accumulation of image detail loss resulting from model inference. In particular, during the initial stages, predicting a clear image from severely degraded input often introduces new blur, over-smoothing, or unnatural textures. These artifacts are propagated to subsequent iterations via Eq. 7 thereby affecting the final restoration.
Let Ta and n. denote the marginal distributions classical static Schrödinger Bridge seeks a coupling π minimizing an entropy-regularize cost as defined in Eq. [9] We enhance this cost by introducing
degraded and clean images, respectively. The
intraadationallinneed term, yielding the
DOT energy:
(11) where D& is a learnable degradation model, and À weights degradation fidelity. Model D& is used to amplify the existing degradations in the image, that is, to learn the inverse process of image restoration. On the one hand, compared artifacts introduced by model predictions, certain natural
CDOT (ma, at.) = ||.. 2
(xx.)) 1
5

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degradation processes. such as haze and rain, are easier to learn. On the other hand, for new types of degradation generated during prediction. amplification makes their differences from the original a more pronounced. Through this component, we impose constraints on the degradations and artifacts we obtain:
produced by the model. Plugging Eq.
11 into Eq.
9
π
arg min ((ma)))~ [CDOT (2r, æt)] 27 H(T).
(12)
To align this with UNSB's s iterative structure, we implement DOT at the selected transport step t,, where Vt, is the intermediate state sampled from the evolving distribution. Let qo (2te//r,,) denote the distribution of generated clean image. We define the DOT loss at step 4 as:
LDOT t,) == Eg (224, me)rut [[| ( )112 A || (
27(1 - tt) H(go (IL, Fc( + KL (ze a Mlp(()))
(13)
4.3 Dynamic Transport with Consistency
DOT imposes the LDOT constraint at a randomly sampled time point 4, However, during the iterative image restoration process, the initial stages are significantly more challenging than the later iterations. Artifacts introduced by the restoration model are also more likely occur in these early stages. Therefore, it is necessary to place greater emphasis on the initial stages during the training of the restoration model. To this end, we further propose Dynamic Transport with Consistency (DTC), which provides supervision at every step of the restoration trajectory.
Specifically, for sampled time point tN., we denote the restoration trajectory as Tuaj {a+to st.....,, We apply LDTT at each step of the trajectory, while the first item in LDT is replaced by LDTC, which is defined as:
Loc = 1 - x (x1,))1 + > || - (D( )
(14)
Here X, is the weight for the degradation-alignmens term, which is computed by
A 1 1 --cos(at)
t E 10.
(15)
Compared with LDOT, CDTC replaces Al| (o((x 12 with Ar, I (xtx. )| The -N--1 X,, /t.// EN Ar.- There are two main reasons learning objective of D ( becomes E/1
behind this modification. First, the (x( in initial stage may contain unnatural scenes, and such representations are not suitable for training the degradation model D&,, whereas the end point of the trajectory Ltx, is of higher quality. In addition, for some steps, the difference between It, and 2t,4; not significant, which also makes them less suitable for training Dz. Therefore, we use weighted average over the entire trajectory as the learning objective, where time steps closer to fN, are assigned higher weights. This approach can, to some extent, reduce the difficulty of degradation learning.
Understanding DTC. In DTC, we enhance the focus on the early stages of the iterative process by supervising the entire trajectory. More importantly, we employ constraint based Dæ( to mitigate the loss of image details during restoration. Compared to using 2i,, (x(x).)) not only incorporates certain restorations upon Tt,, but also amplities the degradations and artifacts introduced by the restoration model, making it more effective constraint. In other words, the transport trajectory is supervised by penalizing the differences between adjacent SB states (i.e., pairwise consistency between H,, and ,,,_,). Compared to baseline UNSB, which only supervises the endpoints, method densely regularizes the entire trajectory, especially the early steps, where errors are more likely to propagate. Therefore, even though the overall loss includes unweighted endpoint terms, the trajectory-leve consistency term explicitly emphasizes earlier stages due to its design, providing stronger guidance when the model most prone to drift.
4.4 Implementation Details
Training Strategy. We randomly select a time step iN, E (to...., tx] and simulate the forward transport from the degraded sample za To obtain {Ii, ..,..... Fix, }. In each intermediate step, Zt; is fed into the conditional generator qo (x,) so as output clean estimate æ.(xx,)

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Together with a reference sample T1, the tuples (zt,, (x),))) and (æee (x()) are used to compute L t.) and DDTC t,). The entropy term is computed by the mutual information neural estimation (MINE) 2 The KI. divergence is implemented via adversarial learning, where Pee and a. (1t,) serve as real and fake inputs, respectively to a Markovian discriminator.
Network Architecture. The conditional generator qe is implemented using a U-Net architecture with instance normalization, where the encoder and decoder consists of five convolutional and deconvolutional layers, respectively. The input and sampled noise are concatenated as the input channels at the first layer, enabling conditioning on both the degraded input and latent noise during the restoration process. The degradation model is lightweight convolutional neural network (CNN), which consists of three 64-channel convolutional layers with ReLU activation functions. Notice that, the degradation model is designed as degradation guidance module rather than a reconstructor. guides the restoration process by penalizing implausible states through constraints on the SB trajectory, making it highly effective for its purpose despite being small.
Hyperparameters. The training terminates after 400 epochs, with a batch size of 1. The initial learning rate is 2 x 10 and decays to zero linearly. All the inputted images are firstly resized to 512 512 pixels and then the image intensity is normalized to [-1, 1]. The time interval [0, 1] is discretized into N uniform steps. The temperature parameter is fixed as T-0.01, and the balanced constant hyper-paramett of LDOT À is set to 0.01. For DTC, the weight of degradation term adopts a cosine annealing schedule. The generator adopts AdaIN layers and sinusoidal timestep embeddings, following DDGAN (50).
5 Experiments
5.1 Results on Multi-Task Image Restoration
Datasets & Evaluation Protocols. We adopt four restoration tasks: deraining, raindrop removal,
deblurring, and low-light enhancement. Rain200L [52] is used for deraining. It includes 1,800
synthetic rainy images for training and 200 for testing. Raindrop [34] is used for raindrop removal. It consists of 1,119 paired images with and without raindrops on glass surfaces. The GoPro dataset (31 is widely used for image deblurring, containing 3,214 high-resolution blurred images (1280x720
pixels). is split into 2.103 samples for training and 1,111 for testing. LOL [48) used for low- light enhancement. It consists of 500 image pairs captured under normal and low-light conditions. Following prior works (20), we use 485 pairs for training and 15 for testing. All images are resized to 512 x 512 pixels and the intensity is normalized before training. These datasets cover a broad spectrum of degradations and provide a comprehensive testbed for multi-task restoration. Following prior unpaired methods 47), during training, for each degraded input image, we randomly sample a clean image from the set, excluding its ground-truth counterpart. The resulting image tuple is thus unaligned and used solely for learning the transport between unpaired distributions. Structural Similarity Index (SSIM) and Peak Signal-to-Notee Ratio (PSNR, in dB), are used for evaluation.
Baselines. We compare DDSB with a wide range of state-of oftt--art- unpaired image restoration methods. These include the classical prior-based approach DCP (16), and various learning- based methods such as CycleGAN [59] YOLY (26]. USID-Net (27. Refine [56], D' [53]. CUT (2).
Santa [5T], ODCR 47). and DN I8] We also include UNSB (22. which formulates cross-domain generation as a Schrödinger Bridge problem. Although Santa, DN, and UNSB were originally proposed for unpaired image translation, we adapt them to image restoration for a boarder comparison. For each task, all the methods are fine-tuned under the same configuration.
Quantitative Evaluation. Table that DDSB achieves the best performance across all four unpaired image restoration tasks. DDSB consistently outperforms all competing unpaired methods in both PSNR and SSIM. Compared with the strongest baseline DN, DDSB achieves significant PSNR gains of +0.69 dB on deraining, +1.12 dB on de-raindrop removal, +1.8 +00 dB on low-light enhancement, and +2.02 dB on deblurring- Corresponding SSIM improvements are +0.025, +0.007, +0.021, and +0.008, respectively. These consistent improvements, especially under challenging conditions like low-light and motion blur, validate the effectiveness of our dynamic Schrödinger Bridge framework with degradation consistency. Furthermore, compared with CUT and D', DDSB demonstrates superior robustness due to its explicit modeling of intermediate transport dynamics and -itadaatioo-alignned consistency.
7

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Table 1: Quantitative comparison of DDSB with the state-of-the-art unpaired image restoration
methods on multi-task restoration. Top three results are highlighted as best
second
and third
Derain
52
Deraindrop
34
Lowlight 48
Deblur
31
Method
PSNR (dB)
SSIM
PSNR (dB)
SSIM
PSNR (dB)
SSIM
PSNR (dB)
SSIM
DCP 16
13.25
0.705
18.92
0.752
15.93
0.743
12.97
0.702
CycleGAN
59
21.28
0.796
20.55
0.787
14.03
0.781
19.10
0.735
YOLY 20
15.72
0.714
14.71
0.748
13.16
0.762
16.28
0.717
USID-Net 28
21.50
0.784
19.81
0.771
17.91
0.769
20.72
0.726
RefineDNet
[56
24.41
0.840
21.65
0.783
19.75
0.793
21.03
0.747
D [53
24.75
0.832
23.84
0.805
21.32
0.826
21.59
0.782
32
24.22
0.815
23.51
0.827
22.90
0,804
21.26
0.766
Santa [1
24.55
0.828
23.65
0.797
21.93
0.838
21.00
0.778
UNSB 22
24.68
0.837
24.52
0.812
22.75
0,822
22.11
0.785
ODCR 47
24.89
0.848
24.08
0.818
23.42
0.832
22.73
0.791
DN [X
24.72
0.845
24.63
0.824
23.58
0.844
23.20
0.796
DDSB (ours)
25.41
0.870
25.75
0.831
25.38
0.865
25.22
0.804
Table Kon-parametric perceptual metric comparison of DDSB with the state-of-the unpaired
image restoration methods. Top three results are highlighted as best
second
and third
Derain
[2
Deraindrop
34
Lowlight
48
Deblur
31
Method
LPIPS
NIQE
LPIPS
NIQE
LPIPS
NIQE
LPIPS
NIQE
DCP [6
0.229
5.37
0.204
5.61
0.218
5.77
0.231
5.94
CycleGAN
0.146
4.82
0.167
4.69
0.197
5.44
0.172
4.98
YOLY
0.198
5.03
0,202
5.19
0,210
0,211
5.47
USID-Net
0.152
4.75
0.172
4.92
5,31
0.162
4.88
RefineDNet 56
0.104
4.36
0.147
4.68
0.179
5.22
0.150
4.71
1 |3
0.098
4.28
0.124
4.50
0.155
5.04
0.139
4.61
CUT 32
0.111
4.42
0.118
4.55
0.142
5.17
0.143
4,66
Santa S
0.096
4.33
0.109
4.39
0.138
5,09
0.130
4.54
UNSB 22
0.085
4.18
0.096
4.27
0.145
5.02
0.126
4.49
ODCR 47
0.076
4.09
0.091
4.21
0.131
4.88
0.121
4.43
DN 18
0.079
4.11
0,082
4.17
0.124
4.85
0.118
4.40
DDSB (ours)
0.063
3.94
0.069
4.03
0.129
4.79
0.108
4.31
Table 3: Quantitative comparison of DDSB with the sfate-of-the-ar unpaired dehazing methods on the generalized dehazing task, trained on SOTS-indoor, and the test result are shown. Cells where results are not available are replaced by "-". The time is measured on images of the size of 512 x 512 pixels using single GPU.
SOTS-ind indoor
25
SOTS outdoor 25
NH-HAZB
Overhead
Method
PSNR (dB)
SSIM
PSNR (dB)
SSIM
PSNR (dB)
SSIM
Para. (M)
Time (ms)
DCP
16
13.10
0.699
19.13
0.815
14,90
0.668
CycleGAN 59
21.34
0.898
20.55
0.856
13.95
0.689
11.38
10.22
YOLY 26
15.84
0.819
14.75
0.857
13.38
0.595
32.00
USID-Net 27
21.41
0.894
23.89
0.919
15.62
0.740
3,780
31.01
RefineDNet
3G
24.36
0.939
19.84
0.853
14.20
0.754
65.80
248.5
D
25.42
25.83
28.08
CUT 52
24.30
0,911
23.67
0.904
15.92
0.758
11.38
10.06
Santa
51
25.01
0,923
24.21
0.945
16.02
0.749
11.43
136
UNSB
25.68
0.930
25.30
0.954
16.10
0.753
14.42
0.212
ODCR
47
26.32
0.945
26.16
0.960
17.56
0.766
11.38
10.14
DN 18
26.25
0.947
26.18
0.962
17.15
0.769
11.40
87.7
DDSB (ours)
27.85
0.956
27.67
0.971
17.92
0.783
14.68
0.019
Non-parametric Perceptual Evaluation. We additionally report two non-parametric metrics that provide a more holistic assessment without relying on predefined statistical models. The Learned Perceptual Image Patch Similarity (LPIPS) measures perceptual distance in deep feature space using a pretrained network and requires ground-trus reference images. The Naturalness Image Quality Evaluator (NIQE) operates without any reference image by modeling natural image statistics. As shown Table 2 we evaluate these two non con-parmetrri metrics on our multi-task restoration benchmark. DDSB consistently outperforms prior methods, demonstrating its strong generalization and perceptual fidelity without withoutrelying relying on pixel-wise supervision.
Qualitative Evaluation. Visual comparisons on four unpaired restoration tasks are shown in Fig. 4 struggles preserve structural details. UNSB yields inconsistent restorations. DN improves local textures, yet residual degradations remain, especially under blur and low-light conditions. ODCR

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Table 4: Ablation study on each compo- nent. Evaluation metrics include PSNR of time step N. and SSIM
Table Impact
Table 6: Impact of Table 7: Impact
of layer depth in
Dø-
SOTS-indoo
EROT
x
Compoment
DOT
DTC
PSNK
27.23
SOTS--iddor
SSIM
0.953
PSNK
SOTS-amnoor
27.04
SSIM
0.963
PSNR
26.91
26.13
0.957
SSIM
0.950
0.943
0.0001
0.001
0.01
27.85
25.76
27:12
SSIM
0.956
0.950
0,940
3
PSNR
27.85
SUTS-indoor
SSIM
0.956
0.96
8
x
26.11
0.947
25.92
0.957
27.85
0.956
0.1
27.34
0.949
0.958
27.85
0.956
27.67
0.971
27.09
0.949
26.91
0,966
26.70
0.933
Input
Raindrop
Low Hight
Figure 3: Comparison of state-of-the-art unpaired methods on multi-task image restoration.
still falters under severe corruption such as dense raindrops or extreme darkness. In contrast, DDSB delivers perceptually sharper and more faithful restorations across all scenarios.
5.2 Results on Generalized Haze Removal
Datasets and Evaluation Protocols. To evaluate the generalization capability of DDSB under diverse
degradation scenarios, we follow the setting of [47] by training the Indoor Training Set (TTS) from RESIDE (25), and evaluating on the SOTS-outdoor (OTS) test set from NH-HAZE 2 [1. which jointly covers synthetic, artificial, and real-world domains. Specifically, RESIDE provides 13,990 synthetic bazy-clear image pairs in ITS and 500 outdoor test pairs in OTS. NH-HAZE 2 contains 25 image pairs with non-homogeneous haze for more challenging and realistic evaluation.
Baselines. We compare DDSB against a broad set of satte-oftthe-ane image dehazing methods. the unpaired setting, include both traditional priors and recent deep models, including DCP [66, Cy- cleGAN [59] CycleDehaze [TI, YOLY [26). USID-Net [27], RefineDNet
(56), D (53] CUT [3), Santa 5I ODCR 47). and DN [18. We also include UNSB [22). Schrödinger
Fridge-based image generation method. Notably, Santa, DN, and UNSB were originally designed for unpaired image generation rather than restoration, and we adapt them dehazing tasks to benchmark their transferability. Following the evaluation protocol of D4, we train all methods on the ITS subset of RESIDE and evaluate on multiple test sets.
Quantitative Evaluation. Table 3 summarizes the performance of DDSB under generalized dehazing protocol. All methods are trained only the SOTS-indoor dataset and evaluated three benchmarks: SOTS-indoor, SOTS- ooTSooutooor and NH-HAZE 2. DDSB achieves the best performance across all settings. In terms of PSNR, DDSB outperforms DN by +1.60 dB on SOTS-indoor, +1.49 dB on SOTS-outdoor, and +0.77 JB on NH-HAZE 2. For SSIM, the improvements are +0.009, +0.009, and +0.014, respectively. These results demonstrate DDSB's 's strong generalization ability to both synthetic and real-world haze conditions. Moreover, DDSB is highly efficient: despite its effectiveness, it only 14.68M parameters and runs 0.019 ms per 512 5122 image significaatlllll faster than most baselines, including DN (87.7 ms) and RefineDNet (248.5 ms).
Qualitative Evaluation. Fig. shows qualitative comparisons. D preserves some scene-level consistency but often leaves residual haze and lacks fine detail recovery. DN introduces texture artifacts and inconsistent brightness in challenging outdoor or real-world scenes. DDSB demonstrates

---

Imput DCP D UNSB
DN
DDSB
Groud Truth
ITS
OTS
NH-
Figure 4: Comparison of state-of-the-ee unpaired methods on generalized haze removal.
the most robust generalization among all compared methods. On SOTSS effectively removes haze while maintaining edge sharpness and color balance. On NH-HAZE 2, DDSB delivers perceptually clean outputs with restored textures, faithful color rendering, and minimal artifacts.
5.3 Ablation Studies
Effeet of Each Component. We conduct an ablation study on the datasets. The results are summarized in Table 4 Starting from the baseline equipped with only EROT, we observe consistent improvements when adding either DOT or DTC. Specifically, DOT brings a PSNR gain +1.55dB on SOTS--ndow and +1.74dB on SOT'S- improvements of +0.023 and +0.009, respectively. When adding DTC alone, PSNR improves by +0.43dB on SOTS- -ind-r and +0.62dB on SOTS-outdoor, and SSIM increases by 0.017 and 0.003, respectively. This shows that DTC improves the intermediate trajectory regularity. Combining DOT and DTC yields the best overall performance, confirming their complementarity.
and SOTS-
as well as SSIM
Effect of Time Step N. Table 3 Jnalyzes how the number of time steps N in the trajectory affects restoration performance. The default setting is N 5. When N is reduced to 3, the performance drops notably (e.g., PSNR drops to 26. 26.18BB at N = 2). When N increases beyond 5 to 6, the performance slightly degrades, likely due to dicceescretinntoon and increased interpolation error.
Effect of Hyper-parametter >. T the sensitivity of our method to the regularization weight À in Eq. 9 which governs the strength of the entropy-regularized transport. We observe that A= = 0.01 achieves the highest performance (27.8 .778 / 0.956).. Setting À too low (e.g., 0.0001) degrades performance significantly (down 25.76dB 0.940), as the EROT constraint becomes too weak. Conversely, overly large À values (e.g.. 1.0) also degrade performance to 26.91dB / 0.946, likely because the transport term dominates and suppresses reconstruction.
Effect of Layer Depth D&. We conduct an ablation study by varying the number convolutional layers in D& from 2 to 7. As shown in Table 7 the 3-layer configuration offers the best trade-off between performance and stability. While the 5-layer variant yields a slightly higher SSIM (0.958), its overall PSNR is marginally lower than the 3-layer setting. The 2-layer model underfits the degradation guidance, and the 7-1ayer version suffers a noticeable performance drop due to training instability.
Conclusion
In this work, we presented Degradation-awarc Dynamic Schrödinger Bridge (DDSB), a novel framework for unpaired image restoration that addresses the limitations of paired data and static restoration dynamics. By leveraging Schrödinger Bridge modeling between unpaired domains and incorporating constraints based on degradation amplification, DDSB enhances the realism of restored outputs. Extensive experiments on diverse degradation scenarios demonstrated the effectiveness and generalizability of our approach, establishing new direction for principled, data-efficient image restoration in real-world settings.
Limitation, Future Work & Societal Impact. DDSB approaches image degradation from machine learning perspective. Some physical degradation models can integrated in the future. This work benefits various image degradation scenarios, and we do not envision its negative societal impact.
10

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A Technical Appendices and Supplementary Material
A.1 Tighter Generalization Error Bound
In this subsection, we provide step-by-step deduction of the generalization error bounds for the proposed Degradation-awen -aware Dynamic Schrödinger Bridge (DDSB), and also demonstrate that has a tighter generalization error bound than the Schrödinger Bridge (SB) baseline.
Definition 1. Generalization Error. The generalization error Egen quantifies the discrepancy between the predicted clean image it and the true clean image Ze., defined as:
Egen
E
[| xell
(16)
where & denotes the clean image generated by the model, and Ie denotes the true clean image.
Lemma 1. Optimal Transport Formulation. The problem of learning the optimal transport plan π² between the degraded image distribution Fa and the clean image distribution Te is formulated as:
arg min (ess.a.) []]=a - xell²] 2T H(TT):
(17)
where H(x) denotes the joint entropy of the transport plan æ, and denotes the regularization hyperparameter.
Proof: Please refer to 13] for the detailed proof. Briefly, the objective is to minimize the discrepancy between Wa and Te while regularizing the transport plan π by its entropy. This ensures that the transport process remains smooth and avoids overfitting. The entropy term H(T) penalizes complex transport plans, promoting a smoother and more generalizable solution.
Theorem 1. Tighter Generalization Error Bound of the Proposed DDSB. Compared to the Schrödinger Bridge baseline, the proposed Degradation-awar Dynamic Schrödinger Bridge (DDSB) has tighter generalization error bound.
Proof: The generalization error is linked to the entropy regularization term H(T). The term N reflects the error due to the finite number of transport steps, while the term T controls the smoothness of the transport plan. As the number of transport steps increases, the transport plan approximates the true coupling between Ta and k.. thus reducing the generalization error. Moreover, increasing reduces the impact of entropy regularization, helping to prevent overfitting and further improving generalization. To summarize, the generalization error for the entropy-regularized optimal transport formulation, i.e. Schrödinger Bridge baseline, bounded as:
CSB 0O (N +
(18)
where N denotes the number of transport steps, and 7 denotes the temperature hyperparameter.
The DDSB method incorporates the degradation-awent term X, which helps the model remain consistent with the degradation process during the restoration. This term reduces error accumulation during the iterative restoration process and improves the generalization performance. The total generalization error is composed of three components: 1. The transport error O (+) which decreases as the number of transport steps increases. 2. The entropy regularization error ( which ensures smooth transport. 3. The degradation fidelity term O()), which helps the restoration process respect the underlying degradation. Thus, the generalization error for DDSB is bounded as:
SO (++++))
cDDSB gon
(19)
Combining Eq. 18 and Eq.
19
we conclude that:
eDDSB
O(A), gen
(20)
demonstrating that the inclusion of the degradation term À results in a tighter error bound for DDSB.
We conclude this subsection by the following remark. This theoretical analysis demonstrates that the proposed DDSB method provides superior generalization performance compared to the SB bascline.
14

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A.2 Connection to Physical Model based Degradation
In this subsection, we provide a theoretical analysis of the Degradation- aware Dynamic Schrödinger Bridge (DDSB), focusing on its connection to degradation-awe aware techniques and the integration of a physical degradation model. This analysis formalizes how the proposed method ensures realistic image restoration by incorporating the degradation process into the transport framework and learning to reverse it.
Degradation-awann aware Transport (DOT) and its Role. The core innovation in DDSB lies in the Degradation Optimal Transport (DOT) term. Traditional Schrödinger Bridge (SB) methods focus on learning transport plan between the degraded and clean image distributions, without considering the physical degradation process that generated the degraded image. DDSB, on the other hand, introduces inngradation-awenn aware component, which ensures that the transport process respects the underlying degradation dynamics at every step.
Let Na and Te denote the degraded and clean image distributions, respectively. The objective in DDSB is learn a transport plan x' that minimizes the discrepancy between these distributions while respecting the degradation model. The optimal transport cost is modified to include the
degradation-aware term:
(D., x:) = | - xel12 + X- (D =
(21)
where Fa a sample from the degraded image distribution TT, w. is a clean image sample, D (xr) denotes the degraded version of æ. predicted by the learned degradation model Dø. and À is hyperparameter controlling the strength of the degradation fidelity term.
The term A- || (xee) æall² enforces that the transport process not only minimizes the discrepancy between æ and c.. but also ensures that the restoration process is consistent with the learned degradation model Dz. This degradation-aware term helps maintain physical realism during the restoration process and prevents the generation of unrealistic artifacts.
Physical Degradation Model De, and its Role. In real-world image restoration, the degradation process is typically complex, involving factors such as noise, blur, and distortion. In many cases, it is impractical to assume simple degradation model (such as Gaussian noise). Therefore, DDSB uses a learnable degradation model D&. which trained to simulate various degradation processes, such as motion blur, fog, and noise. The model D& learns to predict the degradation process for given clean image, providing a more accurate representation of real-world degradation dynamics.
The degradation model D& is integrated into the transport process by penalizing discrepancies between the degraded version of the predicted clean image and the degraded input image. Specifically, at each transport step, we introduce a degradation consistency term that ensures the restored image æ. remains aligned with the degradation process each intermediate step. This term is added the transport cost as follows:
Loo = (ms)) [| - (<(2)) + (x - xx
(22)
where æa a degraded sample, (xa) denotes the predicted clean image at a given transport step, and (z(x((<x)) denotes the degraded version of (x.) predicted by the degradation model Do.
This ensures that each intermediate image in the restoration trajectory follows the degradation process as closely as possible, improving the physical realism of the restoration.
Degradation Amplification for Realism. In this approach, the degradation model D₂ is not only used to predict the degradation but is also employed to amplify the degradation at cach step. This means that the model simulates the inverse of the restoration process by artificially degrading the predicted clean image, making the difference between the degraded image æa and the predicted clean image more pronounced. This helps in preventing the model from generating unrealistic images that would not correspond to any physical degradation.
Formally, the degradation model D& is learned to amplify the degradation, i.e., simulate the inverse process of restoration. The objective is to penalize large deviations between the degraded input æ, and the predicted clean image F. by introducing a degradation consistency term, as described in the DOT loss:
[[D(( xxll?
(23)
15

---

which ensures that the model's 's restoration trajectory remains consistent with the degradation process, leading to more realistic results.
Integrating the Degradation Model into the Transport Process, The key idea behind DDSB is to integrate the degradation model D& into the optimal transport framework. The method learns transport plan x² that minimizes the distance between the degraded and clean images while ensuring that intermediate steps the restoration process respect the physical degradation dynamics. This is achieved by adding the degradation-awee term to the transport cost.
At each step of the restoration, aim align the transport plan with the degradation process. The total loss for DDSB can be expressed as the sum of the standard SB loss and the degradation-awer term:
LDsSB = LsB + LDOT,
(24)
where LsB denotes the standard Schrödinger Bridge loss (transport loss). addition, LDOT denotes the degradation-awar optimal transport loss, which ensures that the restoration process respects the degradation model Da-
This dual loss function encourages the model to minimize the transport cost while ensuring that the restored images are consistent with the degradation process, leading to more realistic and physically plausible restoration results.
We conclude this subsection by the following remark. The introduction of the degradation- term À in the DOT loss improves the generalization of the restoration model. By enforcing consistency with the degradation process, DDSB ensures that the model can generalize well to unseen degradation types. This also reduces the risk of generating unrealistic artifacts, which is common problem in unpaired image restoration tasks.
The Degradation-awarr Dynamic Schrödinger Bridge (DDSB) method introduces novel integration of degradation-aware optimal transport and physical degradation model. By incorporating the degradation model D3 into the transport process, DDSB ensures that the restoration trajectory remains consistent with the physical degradation process, improving the realism of the restored images. This is achieved by penalizing discrepancies between the degraded input and the predicted clean images, leading to a more physically plausible restoration process that reduces artifacts and improves generalization to unseen degradation types.
This theoretical analysis, along with the introduced degradation-awee -warr and dynamic transport compo- nents, lays the foundation for DDSB's 's superior performance in unpaired image restoration, addressing the key challenges of realism and generalization.
B
More Visual Results
B.1
On Multi Task Image Restoration
More visual results of multi-task image restoration are provided in Fig. 5 and Fig. 6
B.2
On Generalized Haze Removal
More visual results of generalized haze removal are provided in Fig. 7 and Fig.
16

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Input
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Figure 5: More results of multi-tass image restoration
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Figure 6: More results of multi task image restoration
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Figure 7: More results of generalized haze removal
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Figure 8: More results of generalized haze removal
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Reviews:
[{"review_id": "BgFZjZDidJ", "reviewer": "Reviewer_dEGW", "summary": "The paper proposes DDSB, a novel unpaired image restoration framework using Schrödinger Bridge modeling and degradation amplification constraints to enhance restored image realism. It shows strong effectiveness and generalizability across various degradation scenarios, offering a new approach for data-efficient restoration.", "questions": "1. The goal of this paper is to address unpaired tasks, but in reality, it still uses paired training datasets. Moreover, these datasets contain many similar scenes (for example, in the GoPro dataset, there are many images with minimal differences). Therefore, it may not be considered strictly unpaired. Additionally, I would like to know how the clear data is sampled during the training process and how to ensure that the training data pairs are strictly unpaired.\n2. This paper employs a diffusion model to tackle the restoration task, thus it is necessary to evaluate it using some non-parametric metrics.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe proposed DDSB method achieves state-of-the-art performance across multiple image restoration tasks, demonstrating strong generalization ability and practical relevance.\n\nWeaknesses:\n1. The current evaluation relies solely on PSNR and SSIM, which is not sufficient. Please consider including several no-reference image quality assessment metrics to better evaluate performance under realistic degradation scenarios.\n2. The results for the denoise task are missing.", "was_revised": true, "final_justification": "The author has addressed my concerns, and I choose to raise my score to 4", "rebuttal": "We thank the reviewer for the positive comments on state-of-the-art performance, strong generalization and practical relevance. The below is a point-by-point response regarding experimental details and analysis.\n\n> **Weakness 1.** *The current evaluation relies solely on PSNR and SSIM, which is not sufficient. Please consider including several no-reference image quality assessment metrics to better evaluate performance under realistic degradation scenarios.*\n\nThanks for your insightful suggestion. Full-reference metrics like PSNR, SSIM, and LPIPS often do not align with human evaluation. Therefore, following [1], we include non-reference metrics MUSIQ [2], CLIP-IQA [3], NIQE [4], and NIMA [5] to better evaluate the results.\n\nWe evaluated DDSB and comparison methods on the NH-HAZE 2 dataset without ground-truth. The results in Table 1 demonstrate DDSB’s superiority not only in signal fidelity (PSNR/SSIM) but also in perceptual quality, validating its robustness and realism under challenging, real-world degradations.\n\n**Table 1. No-reference IQA metrics on NH-HAZE 2.**\n| Method         | CLIP-IQA ↑ | MUSIQ ↑  | NIMA ↑   | NIQE ↓   |\n|----------------|------------|----------|----------|----------|\n| DCP            | 0.236      | 50.682   | 4.311    | 5.668    |\n| CycleGAN       | 0.174      | 21.597   | 3.460    | 5.935    |\n| YOLY           | 0.221      | 48.191   | 4.264    | 6.632    |\n| USID-Net       | 0.227      | 49.033   | 4.234    | 4.613    |\n| RefineDNet     | 0.159      | 24.324   | 3.473    | 6.621    |\n| D⁴             | 0.417      | 56.866   | 4.791    | 3.621    |\n| CUT            | 0.421      | 57.081   | 4.843    | 3.617    |\n| Santa          | 0.485      | 56.035   | 4.827    | 3.523    |\n| UNSB           | 0.508      | 53.987   | 4.915    | 4.423    |\n| ODCR           | 0.498      | 57.689   | 4.954    | 3.736    |\n| DN             | 0.494      | 59.789   | 4.955    | 3.218    |\n| **DDSB (Ours)**| **0.546**  | **62.278** | **4.993** | **2.477** |\n\n---\n  \n> **Weakness 2.** *The results for the denoise task are missing.*\n\nPer your suggestion, we've added the denoising experiment using the SIDD dataset under the unpaired setting. As shown in Table 2, DDSB achieves state-of-the-art performance on the denoising task.\n\n**Table 2. Quantitative comparison of DDSB with the unpaired SOTAs on multi-task restoration.**\n| Method        | Derain (PSNR / SSIM) | Deraindrop (PSNR / SSIM) | Lowlight (PSNR / SSIM) | Deblur (PSNR / SSIM) | Denoise (PSNR / SSIM) |\n|---------------|---------------------|--------------------------|------------------------|----------------------|------------------------|\n| DCP           | 13.25 / 0.705       | 18.92 / 0.752            | 15.93 / 0.743          | 12.97 / 0.702        | 15.55 / 0.731       |\n| CycleGAN      | 21.28 / 0.796       | 20.55 / 0.787            | 14.03 / 0.781          | 19.10 / 0.735        | 21.47 / 0.762   |\n| YOLY          | 15.72 / 0.714       | 14.71 / 0.748            | 13.16 / 0.762          | 16.28 / 0.717        | 17.05 / 0.740      |\n| USID-Net      | 21.50 / 0.784       | 19.81 / 0.771            | 17.91 / 0.769          | 20.72 / 0.726        | 22.36 / 0.761    |\n| RefineDNet    | 24.41 / 0.840       | 21.65 / 0.783            | 19.75 / 0.793          | 21.03 / 0.747        | 23.14 / 0.770   |\n| D⁴            | 24.75 / 0.832       | 23.84 / 0.805            | 21.32 / 0.826          | 21.59 / 0.782        | 24.03 / 0.775          |\n| CUT           | 24.22 / 0.815       | 23.51 / 0.827            | 22.90 / 0.804          | 21.26 / 0.766        | 24.48 / 0.785          |\n| Santa         | 24.55 / 0.828       | 23.65 / 0.797            | 21.93 / 0.838          | 21.80 / 0.778        | 25.28 / 0.793          |\n| UNSB          | 24.68 / 0.837       | 24.52 / 0.812            | 22.75 / 0.822          | 22.11 / 0.785        | 25.11 / 0.799          |\n| ODCR          | 24.89 / 0.848       | 24.08 / 0.818            | 23.42 / 0.832          | 22.73 / 0.791        | 25.60 / 0.805          |\n| DN            | 24.72 / 0.845       | 24.63 / 0.824            | 23.58 / 0.844          | 23.20 / 0.796        | 26.03 / 0.812          |\n| **DDSB (Ours)** | **25.41 / 0.870**   | **25.75 / 0.831**        | **25.38 / 0.865**      | **25.22 / 0.804**    | **26.89 / 0.824**      |\n\n---\n\n> **Question 1.** *The goal of this paper is to address unpaired tasks, but in reality, it still uses paired training datasets. Moreover, these datasets contain many similar scenes (for example, in the GoPro dataset, there are many images with minimal differences). Therefore, it may not be considered strictly unpaired. Additionally, I would like to know how the clear data is sampled during the training process and how to ensure that the training data pairs are strictly unpaired.*\n\nThank you for your insightful questions. \n\n**Similar Scenes:** Regarding the concern that the GoPro dataset contains visually similar scenes due to its origin from video sequences, we acknowledge that some adjacent frames may exhibit high structural similarity. However, we humbly point out that this characteristic is specific to GoPro and not prevalent in other datasets used in our study, such as Rain200L, LOL, and NH-HAZE2, where the image content varies more significantly. Despite this, our method still demonstrates robust performance across all benchmarks, which indicates that DDSB is not dependent on paired or pixel-level correspondence. Instead, DDSB models the restoration process as a distributional alignment using Schrödinger Bridge stochastic dynamics. This formulation inherently avoids reliance on pixel-wise supervision, thus can generalize well even under the unpaired setting.\n\n**Sampling Strategy:** While some datasets (e.g., Rain200L, LOL) do provide paired images, our training procedure strictly avoids using any pairwise information. Following prior unpaired methods D$^{4}$ and ODCR, during training, for each degraded input image $\\boldsymbol{x}_d^{i}$, we randomly sample a clean image $\\boldsymbol{x}_c$ from the set, excluding its ground-truth counterpart $\\boldsymbol{x}_c^i$. The resulting image tuple $(\\boldsymbol{x}_d^i, \\boldsymbol{x}_c^j)$ is thus unaligned and used solely for learning the transport between unpaired distributions. This guarantees that no pixel- or structure-level pairing is used during training. To ensure further robustness, we perform two sanity checks: (1) the clean image set is randomly shuffled once before training to prevent persistent matching patterns; and (2) we explicitly verify that no image is ever matched with its original ground-truth counterpart throughout training. This strategy is consistently applied across all datasets and will be clarified in Section 4.4 (Implementation Details), with additional explanation in Section 5.1 and 5.2 to highlight the strictly unpaired training setup.\n\n---\n  \n> **Question 2.** *This paper employs a diffusion model to tackle the restoration task, thus it is necessary to evaluate it using some non-parametric metrics.*\n\nThank you for the insightful suggestion. We agree that evaluating diffusion-based restoration models requires going beyond traditional parametric metrics such as PSNR and SSIM, which rely on strong assumptions about pixel-wise or structural alignment and often fail to reflect perceptual quality or distributional realism in unpaired settings.\n\nTo this end, we additionally report two non-parametric metrics that provide a more holistic assessment without relying on predefined statistical models: **(1) LPIPS** which measures perceptual distance in deep feature space using a pretrained network and requires ground-truth reference images; and **(2) NIQE** which operates without any reference image by modeling natural image statistics. These two metrics offer complementary insights into perceptual quality LPIPS focuses on semantic similarity to reference targets, while NIQE assesses image naturalness in a fully reference-free manner. As shown in Table 3, we evaluate these two non-parametric metrics on our multi-task restoration benchmark. DDSB consistently outperforms prior methods, demonstrating its strong generalization and perceptual fidelity without relying on pixel-wise supervision.\n\n**Table 3. Non-parametric perceptual metrics on multi-task restoration.**\n\n| Method        | Derain (LPIPS / NIQE) | Deraindrop (LPIPS / NIQE) | Lowlight (LPIPS / NIQE) | Deblur (LPIPS / NIQE) | Denoise (LPIPS / NIQE) |\n|---------------|------------------------|------------|----------|--------|----------|\n| DCP           | 0.229 / 5.37 | 0.204 / 5.61 | 0.218 / 5.77 | 0.231 / 5.94 | 0.248 / 6.10 |\n| CycleGAN      | 0.146 / 4.82 | 0.167 / 4.69 | 0.197 / 5.44 | 0.172 / 4.98 | 0.158 / 5.12 |\n| YOLY          | 0.198 / 5.03 | 0.202 / 5.19 | 0.210 / 5.66 | 0.211 / 5.47 | 0.234 / 5.72 |\n| USID-Net      | 0.152 / 4.75 | 0.172 / 4.92 | 0.188 / 5.31 | 0.162 / 4.88 | 0.149 / 4.96 |\n| RefineDNet    | 0.104 / 4.36 | 0.147 / 4.68 | 0.179 / 5.22 | 0.150 / 4.71 | 0.132 / 4.85 |\n| D⁴            | 0.098 / 4.28 | 0.124 / 4.50 | 0.155 / 5.04 | 0.139 / 4.61 | 0.123 / 4.78 |\n| CUT           | 0.111 / 4.42 | 0.118 / 4.55 | 0.142 / 5.17 | 0.143 / 4.66 | 0.129 / 4.91 |\n| Santa         | 0.096 / 4.33 | 0.109 / 4.39 | 0.138 / 5.09 | 0.130 / 4.54 | 0.118 / 4.76 |\n| UNSB          | 0.085 / 4.18 | 0.096 / 4.27 | 0.145 / 5.02 | 0.126 / 4.49 | 0.116 / 4.73 |\n| ODCR          | 0.076 / 4.09 | 0.091 / 4.21 | 0.131 / 4.88 | 0.121 / 4.43 | 0.109 / 4.69 |\n| DN            | 0.079 / 4.11 | 0.082 / 4.17 | 0.124 / 4.85 | 0.118 / 4.40 | 0.102 / 4.66 |\n| **DDSB (Ours)** | **0.063 / 3.94**  | **0.069 / 4.03** | **0.129 / 4.79** | **0.108 / 4.31** | **0.091 / 4.52** |\n\n[1] Scaling up to excellence: Practicing model scaling for photo-realistic image restoration in the wild.\n\n[2] Musiq: Multi-scale image quality transformer.\n\n[3] Exploring clip for assessing the look and feel of images.\n\n[4] Making a “completely blind” image quality analyzer.\n\n[5] NIMA: Neural image assessment."}, {"review_id": "TtT1G8BwMi", "reviewer": "Reviewer_wJj7", "summary": "The paper proposes a novel method called Degradation-aware Dynamic Schrödinger Bridge (DDSB) for unpaired image restoration. It utilizes the Schrödinger Bridge (SB) framework to map degraded image distributions to clean ones without requiring paired training data. The approach introduces two key innovations: Degradation-aware Optimal Transport (DOT), which integrates a degradation model to minimize error accumulation, and Dynamic Transport with Consistency (DTC), which ensures consistency across the restoration process, particularly addressing early-stage artifacts. The method is evaluated on tasks such as denoising, deraining, deblurring, and dehazing, achieving state-of-the-art performance with strong generalization to unseen degradation types.", "questions": "See the points in Weakness. Especially the firts point for difference with existing method.", "limitations": "yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1. The proposed DOT enhances restoration realism by incorporating degradation priors, a significant improvement over existing unpaired methods that often overlook physical degradation processes. And DTC’s focus on maintaining consistency throughout the restoration trajectory, especially in early stages, reduces artifacts and improves output quality.\n2. The proposed method demonstrates superior results across multiple tasks, with notable PSNR gains (e.g., up to 1.60 dB over baselines) and efficient inference (0.019 ms per 512x512 image), supported by extensive empirical validation.\n\nWeaknesses:\n1. The most crucial issue is the novelty of the proposed framework. Since Schrödinger bridge has been used in unpaired image restoration learning [1]. This paper seems to extend Schrödinger bridge to multiple degradation types, while [1] only focuses on image deraining. \n[1] Neural Schrödinger bridge for unpaired real-world image deraining, information sciences 2024. \n\n2. DOT’s success hinges on the accuracy of the degradation model. If the degradation is complex, non-linear, or poorly estimated, performance could suffer. The paper does not test DDSB’s robustness to imperfect degradation models, leaving its reliability uncertain in real-world scenarios with unknown or mixed degradations.\n\n3. Comparisons are restricted to unpaired methods, omitting state-of-the-art supervised approaches. Including these would contextualize the trade-offs of using unpaired data and reveal whether DDSB narrows the gap with supervised performance", "was_revised": true, "final_justification": "My previous cocerns on motivation and more experiments validation have been well addressed.", "rebuttal": "We thank the reviewer for the positive comments on its significant improvement and superior performance. The below is a point-by-point response regarding its technical significance, performance on more complex degradations and more methodology comparison.\n\n> **Weakness 1.** *The most crucial issue is the novelty of the proposed framework. Since Schrödinger bridge has been used in unpaired image restoration learning [1]. This paper seems to extend Schrödinger bridge to multiple degradation types, while [1] only focuses on image deraining.*\n*[1] Neural Schrödinger bridge for unpaired real-world image deraining, Information Sciences 2024.*\n\nWe thank the reviewer for pointing out the connection to Neural Schrödinger Bridge (NSB) [1]. Our Degradation-aware Dynamic Schrödinger Bridge (DDSB) is positioned as a principled extension of the SB paradigm along five axes:\n\n**Extension to Multiple Degradation Types:** NSB presents a valuable framework tailored for real-world image deraining. Inspired by its success, our DDSB framework is designed with broader applicability in mind and is evaluated across four representative degradation types (deblurring, dehazing, low-light enhancement, and deraining) on five benchmarks. This multi-degradation formulation is intended to assess the generalization ability of SB-based restoration models in more varied and challenging settings.\n\n**Dynamic Multi-Step Transport Modeling:** Instead of adopting a one-shot transport from degraded to clean domains, DDSB is formulated as a discrete-time, multi-step Markov process. This dynamic modeling captures the temporal evolution of the restoration trajectory and enables progressive refinement over time. We found this design particularly beneficial in handling severe degradations and complex distribution shifts.\n\n**Integration of Degradation-Aware Guidance:** To better inform the restoration process, we incorporate a learnable degradation model into the cost structure of the SB formulation. This component estimates inverse degradations and serves as a guidance signal throughout the transport trajectory. This dynamic coupling between degradation estimation and transport provides task-adaptive control without requiring explicit paired supervision.\n\n**Consistency across Transport Trajectory:** We propose a trajectory consistency regularization mechanism that aligns intermediate transport states with degradation-inverted outputs. This design aims to encourage stable transitions and mitigate potential semantic drifts during dynamic transport. We found this consistency particularly helpful when dealing with longer or more complex SB trajectories.\n\n**Theory-Grounded Extensibility:** DDSB is derived from both the stochastic control and static SB perspectives and is grounded in entropy-regularized optimal transport. This theoretical foundation supports modular extensions, such as degradation-aware transport and trajectory consistency, which can be beneficial for future extensions of SB-based restoration methods.\n\nIn summary, while NSB provides a strong foundation for applying Schrödinger Bridge to image deraining, our work aims to systematically extend this direction by introducing dynamic transport, learnable degradation modeling, and cross-time consistency, enabling broader applicability and improved generalization. We will clarify this relationship and cite [1] more prominently in the revised version.\n\n---\n  \n> **Weakness 2.** *DOT’s success hinges on the accuracy of the degradation model. If the degradation is complex, non-linear, or poorly estimated, performance could suffer. The paper does not test DDSB’s robustness to imperfect degradation models, leaving its reliability uncertain in real-world scenarios with unknown or mixed degradations.*\n \nThanks for your insightful question regarding the inaccurate or non-identifiable degradation models, particularly in real-world settings with complex or unknown degradations.  \nTo clarify, technically, the proposed method is effective to handle such challenges due to the following properties.\n\n**Design Rationale:** While the Degradation-aware Optimal Transport (DOT) module introduces a learnable degradation model $D_\\phi$ into the SB framework, it is important to note that $D_\\phi$ is not treated as a standalone predictor or inference-time component. Instead, it functions as a soft constraint on the SB trajectory during training, and is optimized jointly with the generator. This setup ensures that DDSB does not rely on explicit degradation labels or priors, making it inherently robust to misspecification.\n\n**Experimental Robustness Evaluation:** To demonstrate the robustness of DDSB under diverse and unknown degradation conditions, we evaluate it on two challenging benchmarks under unpaired setting: the Under-Display-Camera (UDC) dataset [2] and the Enhancing Underwater Visual Perception (EUVP) dataset [3]. Both datasets encompass a variety of unknown image degradations, enabling a comprehensive assessment of DDSB’s capability to generalize across different distortion types. Specifically, for EUVP, we adopt the unpaired subset to better reflect real-world restoration scenarios.\n\n**Table 1: Quantitative comparison of DDSB with the state-of-the-art unpaired image restoration methods on multiple unknown degradations (non-reference metrics).**\n| Method           | MUSIQ ↑ (UDC) | CLIP-IQA ↑ | NIQE ↓ | NIMA ↑ | MUSIQ ↑ (EUVP) | CLIP-IQA ↑ | NIQE ↓ | NIMA ↑  |\n|------------------|---------------|-------------------|--------------|---------------|------------------|--------------------|----------------|----------------|\n| DCP              | 34.65         | 0.218             | 8.735        | 3.821         | 32.10            | 0.212              | 8.890          | 3.794          |\n| D⁴               | 42.43         | 0.274             | 7.110        | 4.144         | 38.47            | 0.261              | 7.508          | 3.982          |\n| CUT              | 42.95         | 0.271             | 7.005        | 4.115         | 39.05            | 0.259              | 7.439          | 3.968          |\n| UNSB             | 43.59         | 0.282             | 6.761        | 4.231         | 39.81            | 0.269              | 7.244          | 4.033          |\n| ODCR             | 44.02         | 0.286             | 6.597        | 4.256         | 40.23            | 0.272              | 7.123          | 4.057          |\n| DN               | 44.55         | 0.292             | 6.483        | 4.279         | 40.58            | 0.278              | 6.994          | 4.081          |\n| **DDSB (ours)**  | **45.78**     | **0.301**         | **6.342**    | **4.325**     | **41.42**        | **0.287**          | **6.875**      | **4.108**      |\n\n\n**Resilience to Imperfect Modeling:** In addition, we found that $D_\\phi$ typically converges to a stable mapping that encourages physical realism rather than exact inversion. Even when $D_\\phi$ is suboptimal, DDSB benefits from its soft regularization role without collapsing. This robustness will be discussed in the final version.\n\n---\n\n> **Weakness 3.** *Comparisons are restricted to unpaired methods, omitting state-of-the-art supervised approaches. Including these would contextualize the trade-offs of using unpaired data and reveal whether DDSB narrows the gap with supervised performance.*\n  \nThanks for your valuable suggestion to include state-of-the-art supervised methods for broader context.  \nTo this end, we conducted additional experiments on the generalized haze removal task using popular supervised methods including DehazeNet [4], AOD-Net [5], PromptIR[6] and AutoDIR[7]. The results are shown in Table 2:\n\n**Table 2: Comparison with supervised methods on GoPro (Deblurring) and LOL (Low-light Enhancement). DDSB achieves competitive performance without using paired supervision.**\n| Supervision| Method   | SOTS-indoor PSNR / SSIM | SOTS-outdoor PSNR / SSIM | NH-HAZE 2 PSNR / SSIM |\n|----------|------------|--------------------------|----------------------------|------------------------|\n| Paired   | DehazeNet  | 19.82 / 0.818            | 24.75 / 0.927              | 10.62 / 0.521          |\n|          | AOD-Net    | 20.51 / 0.816            | 24.14 / 0.920              | 12.33 / 0.631          |\n|          | PromptIR   | **28.63 / 0.962**        | 27.85 / 0.973              | 18.26 / 0.786          |\n|          | AutoDIR    | 28.42 / 0.962            | **27.93 / 0.975**          | **18.95 / 0.787**      |\n| Unpaired | UNSB       | 25.68 / 0.930            | 25.30 / 0.954              | 16.10 / 0.753          |\n|          | ODCR       | 26.32 / 0.945            | 26.16 / 0.960              | 17.56 / 0.766          |\n|          | DN         | 26.25 / 0.947            | 26.18 / 0.971              | 17.15 / 0.769          |\n|          | **DDSB**   | **27.85 / 0.956**        | **27.67 / 0.971**          | **17.92 / 0.783**      |\n\nDespite operating in the unpaired setting, DDSB substantially closes the performance gap with supervised models. This highlights DDSB’s capacity to learn robust mappings from distributional alignment without requiring pixel-level supervision. We will include this comparison in the final manuscript (Section 5).\n\nShould you have further questions or comments, we are glad to address during the author-reviewer discussion stage.\n\n[1] Neural Schrödinger bridge for unpaired real-world image deraining. Information Sciences 2024.\n\n[2] Image restoration for under-display camera. CVPR2021.\n\n[3] Fast underwater image enhancement for improved visual perception. IEEE Robotics and Automation Letters.\n\n[4] Dehazenet: An end-to-end system for single image haze removal. IEEE TIP.\n\n[5] AOD-Net: All-in-one dehazing network. ICCV2017.\n\n[6] Promptir: Prompting for all-in-one image restoration. NeurIPS2023.\n\n[7] Autodir: Automatic all-in-one image restoration with latent diffusion. ECCV 2024."}, {"review_id": "e6SDilITXk", "reviewer": "Reviewer_vpkm", "summary": "The paper introduces a Degradation-aware Dynamic Schrödinger Bridge (DDSB) for unpaired image restoration. By combining the Schrödinger Bridge framework with degradation-aware optimal transport and dynamic consistency, DDSB can handle image degradation without requiring paired data. It incorporates a degradation model to reduce error accumulation and improve restoration quality through iterative refinement. Experiments show that DDSB outperforms existing unpaired restoration methods.", "questions": "1. Table2 shows that the proposed method takes only 0.019ms to process an image , which is very fast. However, the proposed approach is clearly an iteration-based scheme, which is reasonably computationally expensive.\n2. As can be seen in Fig2, the degradation-aware Optimal Transport has only three layers of convolution in the degradation-aware model, how does such a small model perform in complex scenes？", "limitations": "This method is not validated in complex real-world scenarios.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n   1. This paper introduces Degradation-aware Dynamic Schrödinger Bridge (DDSB) for unpaired image restoration.\n   2. The DOT  strategy helps reduce the artifact accumulation.\n   3. The writing is easy to follow.\n\nWeaknesses:\n   1. For real multi-degradation scenarios, despite the DTC strategy is employed, training stability remains an issue. The early iterations may still generate artifacts, which could be propagated through the network.\n   2. Poor implementation details, e.g. Qϕ and Dϕ do not give relevant implementation details.\n   3. DDSB relies heavily on hyperparameters, and this sensitivity requires a large number of adjustments.", "was_revised": true, "final_justification": "Most of my concerns have been addressed, but I still have doubts about the results in real multi-degradation coupling scenarios. Thus, I tend to keep the original score.", "rebuttal": "We thank the reviewer for the positive comments on its method design, effectiveness to reduce artifact accumulation and writing. The below is a point-by-point response addressing the training stability, implementation details and hyperparameter sensitivity. \n\n> **Weakness 1.** *For real multi-degradation scenarios, despite the DTC strategy is employed, training stability remains an issue. The early iterations may still generate artifacts, which could be propagated through the network.*\n \nWe fully agree that artifact accumulation in the early stages poses a significant challenge in multi-degradation scenarios. Below, we elaborate on how this challenge is tackled from both methodological and empirical perspectives.\n\n**Emphasis on Early-Stage Consistency:** While Eq.(14) employs a cosine-scheduled weight that increases towards the final step ($t \\rightarrow 1$), this does not imply that early stages receive negligible guidance. Rather, the DTC module applies **pairwise consistency constraints** between adjacent trajectory steps (e.g., $x_{t_1}$ and $x_{t_2}$), such that early transitions are more tightly regularized. Compared to prior work like UNSB, which only constrains the endpoint, our design provides denser and earlier guidance.\n\n**Empirical Verification:** We validated this enhanced DDSB variant on a synthetic “combo degradation” benchmark combining blur, rain, and low-light degradations. Below is the comparison of intermediate trajectory quality (average PSNR at $t_1$, $t_2$, $t_3$):\n\n**Table1: Intermediate PSNR at early SB steps on mixed degradation. DTC + denoise regularization improves early-stage stability.**\n| Method                           | $t_1$ ↑ | $ t_2$ ↑ | $t_3$ ↑ |\n|----------------------------------|----------|----------|----------|\n| DDSB w/o DTC | 17.96 | 21.40 | 24.22 |\n| DDSB + DTC | 19.38 | 23.15 | 26.09 |\n\n---\n\n> **Weakness 2.** *Poor implementation details, e.g. $q_\\phi$ and $D_\\phi$ do not give relevant implementation details.*\n\nPer your suggestion, we've added the following implementation details regarding the generator $q_\\phi$ and degradation model $D_\\phi$.\n\n**Generator $q_\\phi$:** The conditional generator $q_\\phi(x_c \\mid x_{t_i})$ is implemented using a U-Net architecture with instance normalization:\n- **Encoder:** 5 convolutional layers with kernel size 3, stride 2, increasing channels from 64 to 512.  \n- **Bottleneck:** 2 residual blocks with dilated convolutions to capture wider receptive fields.  \n- **Decoder:** 5 deconvolutional layers with skip connections from the corresponding encoder layers.  \n- **Conditioning:** The input $x_{t_i}$ and sampled noise are concatenated as input channels at the first layer, enabling conditioning on both the degraded input and latent noise during the restoration process.\n\n**Degradation Model $D_\\phi$:** The degradation model $D_\\phi$ is a lightweight CNN inspired by the DnCNN encoder:\n- **Layers:** 3 convolutional layers with ReLU activations and 64 channels.  \n- **Output:** The output is a full-resolution image designed to approximate the degraded observations $x_d$.  \n- **Training:** The model is trained jointly with $q_\\phi$ in a way that does not require explicit degradation labels, making it applicable to unpaired restoration tasks.\n\n---\n\n> **Weakness 3.** *DDSB relies heavily on hyperparameters, and this sensitivity requires a large number of adjustments.*\n\nThanks for your insightful question. DDSB introduces several loss weights (e.g., $\\lambda$, $\\tau$, and $\\lambda_{t_i}$).\n\n**Default configuration is generalizable:**  Used fixed hyperparameters across all tasks:\n- $\\tau = 0.01$ (entropy weight) \n- $\\lambda = 0.01$ (DOT alignment)   \n- $\\lambda_{t_i} \\in [0, 0.01]$ (cosine-scheduled DTC)\n\nThese were tuned only once on Rain200L and fixed for all other datasets.\n\n**Ablation study on sensitivity:** To address the concern about the sensitivity of DDSB to hyperparameters, we provide an ablation study that investigates the impact of the alignment weight $\\lambda$ and the temperature parameter $\\tau$. The following Table1 (Table 5 of the original paper) summarizes the sensitivity of DDSB to the alignment weight $\\lambda$.\n\n**Table 1. Impact of hyper-parameter $\\lambda$**\n| $\\lambda$  | PSNR | SSIM  |\n|------------|------|-------|\n| 0.0001| 25.76 | 0.940 |\n| 0.001| 27.12 | 0.950 |\n| 0.01| **27.85** | **0.956** |\n| 0.1| 27.24 | 0.949 |\n| 1| 26.91 | 0.946 |\n\nAn addtional ablation study was conducted to analyze the effect of $\\tau$ with the optimal value of $\\lambda = 0.01$. Below is a summary of the PSNR and SSIM performance for various values of $\\tau$ on the SOTS-indoor dataset.\n\n**Table 2. Impact of hyper-parameter $\\tau$**\n| $\\tau$  | PSNR / SSIM |\n|---------|-------------|\n| 0.005 | 26.82 / 0.943 |\n| 0.01 | **27.85** / **0.956** |\n| 0.02 | 27.49 / 0.952 |\n| 0.05 | 27.08 / 0.943 |\n\nThe sensitivity of $\\tau$ demonstrates that small adjustments around the optimal values yield consistent performance.\n\n---\n\n> **Question 1.** *Table2 shows that the proposed method takes only 0.019ms to process an image, which is very fast. However, the proposed approach is clearly an iteration-based scheme, which is reasonably computationally expensive.*\n\nThank you for your insightful question. We agree that DDSB is an iterative approach in theory, but we want to emphasize that the **iterative process is only applied during the intermediate steps** of the Stochastic Schrödinger Bridge (SB) trajectory. This design ensures that DDSB can maintain high computational efficiency without incurring large overheads from full iterative processing.\n\n**Efficient Iterative Process:** During inference, DDSB leverages a **single deterministic SB trajectory**, where only the intermediate steps (typically 4 steps) are computed iteratively. In other words, only the parameters of a light-weight U-Net are involved during the entire iterations. Besides, the input of the U-Net is the latent embedding, which has a much smaller size than the original image. Both aspects allows us to significantly reduce computational overhead compared to fully iterative methods.\n\n**Computational Efficiency:** The generator $q_\\phi$ and degradation model $D_\\phi$ are both lightweight, making the entire model fast and suitable for real-time applications.\n\n---\n\n> **Question 2.** *The degradation-aware model only uses 3 convolution layers. How can such a small model perform in complex scenes?*\n\nThanks for your insightful question regarding the efficiency of the degradation-aware model, particularly given its lightweight architecture.\n\n**Role as Regularizer:** $D_\\phi$ is designed as a degradation guidance module, not a reconstructor. It does not generate images but instead guides the restoration process by penalizing implausible states through constraints on the SB trajectory. Its role is focused on guiding the network, making it highly effective for its purpose despite being small.\n\n**Lightweight Design Enhances Stability:** While deeper models may introduce instability into the dynamic training process, $D_\\phi$'s 3 convolution layers balance expressiveness and stability. Deeper networks could destabilize the Schrödinger Bridge process by introducing excessive noise or overfitting, particularly in early stages of training, where the model is more sensitive.\n\n**Experimental Performance in Complex Scenes:** To demonstrate the robustness of Degradation-Aware Model ($D_\\phi$) under diverse and unknown degradation conditions, we evaluate DDSB on two challenging benchmarks under unpaired setting: the UDC dataset [1] and EUVP dataset [2]. Both datasets encompass a variety of unknown image degradations.\n\n**Table 3. Quantitative comparison of DDSB with the state-of-the-art unpaired image restoration methods on multiple unknown degradations (non-reference metrics).**\n| Method | MUSIQ ↑ (UDC) | CLIP-IQA ↑ | NIQE ↓ | NIMA ↑ | MUSIQ ↑ (EUVP) | CLIP-IQA ↑ | NIQE ↓ | NIMA ↑  |\n|------------------|---------------|-------------------|--------------|---------------|------------------|--------------------|----------------|----------------|\n| DCP | 34.65 | 0.218| 8.735 | 3.821 | 32.10| 0.212  | 8.890 | 3.794 |\n| D⁴| 42.43| 0.274 | 7.110 | 4.144 | 38.47 | 0.261 | 7.508 | 3.982 |\n| CUT | 42.95| 0.271| 7.005 | 4.115 | 39.05| 0.259  | 7.439 | 3.968 |\n| UNSB| 43.59 | 0.282| 6.761 | 4.231| 39.81 | 0.269 | 7.244 | 4.033 |\n| ODCR| 44.02 | 0.286 | 6.597 | 4.256 | 40.23 | 0.272  | 7.123 | 4.057 |\n| DN | 44.55| 0.292  | 6.483 | 4.279| 40.58 | 0.278 | 6.994 | 4.081 |\n| **DDSB (ours)**  | **45.78**  | **0.301** | **6.342**| **4.325** | **41.42** | **0.287**| **6.875** | **4.108** |\n\n**Ablation study on layer depth in $D_\\phi$:** To evaluate the effectiveness of our lightweight degradation-aware design, we conduct an ablation study by varying the number of convolutional layers in $D_\\phi$ from 2 to 7. All experiments are performed on the SOTS-indoor dataset.\n\n| Conv Layers | PSNR / SSIM |\n|-------------|---------------------|\n| 2 layers    | 25.37 / 0.926       |\n| **3 layers**| **27.85** / 0.956 |\n| 5 layers    | 27.69 / **0.958**    |\n| 7 layers    | 26.70 / 0.933       |\n\nAs shown in Table 4, the 3-layer configuration offers the best trade-off between performance and stability. While the 5-layer variant yields a slightly higher SSIM (0.958), its overall PSNR is marginally lower than that of the 3-layer setting. The 2-layer model underfits the degradation guidance, and the 7-layer version suffers a noticeable performance drop due to training instability. This balance between model capacity and stability further justifies the final design of $D_\\phi$ and will be discussed in detail in Section 4.4.\n\nShould you have further questions, we are glad to address in the author-reviewer discussion stage.\n\n[1] Image restoration for under-display camera. CVPR2021.\n\n[2] Fast underwater image enhancement for improved visual perception. IEEE Robotics and Automation Letters."}, {"review_id": "Er0bXnoHOs", "reviewer": "Reviewer_D1L2", "summary": "This paper presented Degradation-aware Dynamic Schrödinger Bridge (DDSB), a novel framework for unpaired image restoration that addresses the limitations of paired data and static restoration dynamics.", "questions": "1. The author should discuss the fundamental connection between DOT and Cyclegan on jointly training restoration and degradation process.\n2. The author needs to give a stronger explanation of DTC section about \"the statement emphasizes the early stage while the implementation weights more towards the later stage\".\n3. The quantitative results presented in the paper are promising. To further strengthen the claims, it would be highly beneficial for the authors to demonstrate the framework's effectiveness on perceptually-aligned metrics, such as FID, LPIPS.", "limitations": "Yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength:\nThis paper apply Schrödinger Bridge to unpaired image restoration task and propose degradation-aware optimal transport and dynamic transport with consistency to the realism of restored outputs. The results on diverse degradation scenarios demonstrated the effectiveness of the proposed methods.\n\nWeakness:\n1. Schrödinger Bridge has been used for unpaired image to image translation, which is similar to unpaired image restoration. While the paper proposes two extensions to the Schrödinger Bridge framework, DOT and DTC, my main concerns are their limited novelty in the context of existing literature.\n2. The core principle of DOT, which involves jointly training a forward process (restoration) and a backward process (degradation) to enforce consistency, is conceptually very similar to cycle-consistency loss of the seminal work on CycleGAN.\n3. In DTC section, this paper stated that “Therefore, it is necessary to place greater emphasis on the initial stages during the training of the restoration model.” However, the proposed weighting schedule in Eq.(14) shows that it assigns near-zero weight to the initial stages (t → 0) and maximum weight to the final stages (t → 1). There is lacking of a careful explanation about this.\n4. This paper should write the loss of EROT in end of Section 4.1 to enhance the clarity.\n5. The q_\\phi(x_c|x_j) in Fig. 2 should be q_\\theta(x_c|x_j)?\n6. The subscript of \\mathbb{E} of Eq.(12) is not complete.\n7. In Eq.(5), why you assign the joint distribution to the marginal distribution, omitting the integral sign by default?", "was_revised": true, "final_justification": "The authors addressed my comments. I decide to keep my borderline accept recommendation.", "rebuttal": "We thank the reviewer for acknowledging the effectiveness of DDSB. Below we provide point-by-point responses to your concerns on novelty, implementation clarity, and conceptual distinctions from prior work.\n  \n> **Weakness 1.** *Schrödinger Bridge has been used for unpaired image to image translation, which is similar to unpaired image restoration. While the paper proposes two extensions to the Schrödinger Bridge framework, DOT and DTC, my main concerns are their limited novelty in the context of existing literature.*\n  \nWe thank the reviewer for pointing out the connection to prior SB-based unpaired translation works. While we acknowledge that Schrödinger Bridge (SB) has been explored in domain transfer tasks, we respectfully argue that our framework introduces **conceptual and technical novelties** tailored specifically for unpaired **image restoration** under mixed degradation uncertainty.\n\n**DOT – Degradation-aware Optimal Transport:** Prior SB works typically assume fixed endpoint distributions (e.g., stylized domain or Gaussian prior). In contrast, our DOT module introduces a **learnable degradation estimator $D_\\phi$**, which dynamically regularizes the transport cost. This enables:  \n- Adaptive constraint on the SB path to align with plausible degradation outcomes;  \n- Enhanced generalization to multiple, unknown degradation types such as haze, rain, or blur (Table 1, Table 2);  \n- A new transport objective (Eq. 9) that is **modulated by $D_\\phi$**, directly influencing the stochastic trajectory and not present in prior SB formulations .\n\n**DTC – Dynamic Transport with Consistency:** While earlier works often supervise only terminal states, our DTC introduces **temporal consistency across intermediate SB steps**:  \n- A cosine-weighted constraint is applied to neighboring states $\\{x_{t_i}\\}$, guiding smoother, progressive transitions;  \n- This alleviates error propagation from early to later stages, which is a major issue in restoration tasks (Table 5);  \n- To our knowledge, such temporal regularization across transport states is novel in the SB literature.\n\n**Restoration vs. Translation – A fundamentally different regime:** Image restoration differs from translation in that:  \n- The source domain (degraded images) is highly noisy and contains compound distortions, whereas translation tasks deal with domain shifts between relatively clean modalities;  \n- Restoration requires **fine-grained reconstruction fidelity**, not merely style/domain alignment, making trajectory regularization via $D_\\phi$ and DTC essential .\n\nIn summary, DOT and DTC introduce nontrivial advances in both the objective formulation and trajectory supervision, addressing challenges **unique to unpaired restoration**. We will explicitly highlight these distinctions and cite relevant SB-based translation works in the revised Related Work and Method sections.\n\n---\n \n> **Weakness 2.** *The core principle of DOT, which involves jointly training a forward process (restoration) and a backward process (degradation) to enforce consistency, is conceptually very similar to cycle-consistency loss of the seminal work on CycleGAN.*\n \nThanks for the insightful question. While DOT and CycleGAN both involve forward and backward mappings, their objectives, formulations, and implementation mechanisms are fundamentally distinct.\n\n**Objective difference:**\n- **CycleGAN** enforces consistency via deterministic reconstruction, i.e., $ x \\rightarrow G(x) \\rightarrow F(G(x)) \\approx x $, assuming clean reversibility between domains.\n- **DOT**, in contrast, aims to constrain *stochastic diffusion paths* in the Schrödinger Bridge (SB) framework through a degradation-aware cost. The backward model $D_\\phi$ is **not** used to reconstruct the original input but to ensure that intermediate samples remain plausible with respect to the degradation distribution.\n\n**Formulation difference:**\n- **CycleGAN** employs an explicit $\\ell_1$ cycle-consistency loss:\n$$\n  \\mathcal{L}_{cyc} = \\mathbb{E}_x \\left[ || F(G(x)) - x ||_1 \\right]\n$$\nThis loss enforces deterministic round-trip reconstruction.\n- **DOT** modifies the SB transport via a degradation-guided regularizer:\n$$\n  \\mathbb{E}_{x_c, \\epsilon} \\left[ || D _\\phi ( q _\\phi (x_c, \\epsilon)) - x_d ||^2 \\right]\n$$\n\nThis guides the **probabilistic sampling path** to be consistent with the degradation distribution, and is integrated into the optimal transport objective.\n\n**Mechanism difference:**\n- **CycleGAN** is a **single-step mapping** trained via adversarial + reconstruction losses, assuming structural reversibility.\n- **DOT** operates within a **multi-step stochastic diffusion process**, where transport trajectories evolve through discrete steps $\\{x_{t_i}\\}$ under SB dynamics. DOT regularizes the **endpoint** of these trajectories to align with a learned degradation prior.\n\n---\n  \n> **Weakness 3.** *In DTC section, this paper stated that “Therefore, it is necessary to place greater emphasis on the initial stages during the training of the restoration model.” However, the proposed weighting schedule in Eq.(14) shows that it assigns near-zero weight to the initial stages (t→0) and maximum weight to the final stages (t→1). There is lacking of a careful explanation about this.*\n\nThank you for your careful reading. We acknowledge that our earlier phrasing may have caused confusion, and we appreciate the opportunity to clarify.\n\nThe reviewer's concern arises from a misunderstanding: the temporal weighting schedule mentioned in Eq.(14) applies specifically to the consistency constraint term in our Dynamic Transport with Consistency (DTC) module—not the overall loss, i.e., the second term of Eq.(12) $\\lambda [|| x _{t_i} - D _\\phi(x _c(x _{t_i})) ||^2]$.\n\nIn DTC, we supervise the transport trajectory by penalizing the differences between adjacent SB states (i.e., pairwise consistency between $x_{t_{i}}$ and $x_{t_{i-1}}$). Compared to baseline UNSB, which only supervises the endpoints, our method densely regularizes the entire trajectory, especially the early steps, where errors are more likely to propagate.\n\nTherefore, even though the overall loss includes unweighted endpoint terms, the trajectory-level consistency term explicitly emphasizes earlier stages due to its design, providing stronger guidance when the model is most prone to drift.\n\n---\n  \n> **Weakness 4.** *This paper should write the loss of EROT in end of Section 4.1 to enhance the clarity.*\n \nThanks for the insightful suggestion. We agree that explicitly stating the EROT loss improves clarity and will revise Section 4.1 accordingly.\n\nThe Entropy-Regularized Optimal Transport (EROT) loss used in our framework is:\n\n$$\n \\mathcal{L}_{EROT} = \\mathbb{E} _{(x _d, x _c) \\sim \\pi} [\\|\\|x_d - x_c\\|\\|^2] - 2\\tau  \\mathcal{H}(\\pi) + \\mathrm{KL}(q _\\theta(x_c) \\|\\| p(x_c)), \\pi \\in \\Pi(\\pi_d, \\pi_c)\n$$\n\nHere, the first term measures the reconstruction error between the predicted clean sample $q _\\phi(x_d)$ and the clean target $x_c$, while the second term ensures distributional regularity via KL divergence. This loss serves as the primary endpoint supervision to guide the restoration trajectory.\n\n---\n  \n> **Weakness 5.** *The $q_\\phi(x_c|x_j)$ in Fig. 2 should be $q_\\theta(x_c|x_j)$?*\n \nYes, we will correct the subscript from $\\phi$ to $\\theta$ in Fig. 2.\n\n---\n  \n> **Weakness 6.** *The subscript of $\\mathbb{E}$ of Eq.(12) is not complete.*\n  \nWe will complete it as:  \n$$\n\\mathbb{E}_{q _{\\theta}(x _{t_i}, x _c)\\sim \\pi}\n$$\n\n---\n  \n> **Weakness 7.** *In Eq.(5), why you assign the joint distribution to the marginal distribution, omitting the integral sign by default?*\n \nThanks for the suggestion. The original Eq.(5) omits the marginalization for brevity, but we agree it may cause confusion.  \nWe will revise it to the full joint form $p( ${$ x_{t_n} $}$ ) = p(x_{t_N} \\mid x_{t_{N-1}}) \\cdots p(x_{t_1} \\mid x_{t_0}) p(x_{t_0})$\n\n---\n  \n> **Question 1.** *The author should discuss the fundamental connection between DOT and CycleGAN.*\n \nSame as Weakness 2.\n\n---\n  \n> **Question 2.** *The author needs to give a stronger explanation of DTC about early vs. later stage weighting.*\n \nSame as Weakness 3.\n\n---\n  \n> **Question 3.** *To further strengthen the claims, please show results on perceptual metrics like FID, LPIPS.*\n  \nThanks for the suggestion. We have added comparison on **FID** and **LPIPS** metrics for multi-task restoration. The results are summarized below:\n\n**Table 1. Perceptual metrics on multi-task restoration.**\n| Method | Derain (FID / LPIPS) | Deraindrop (FID / LPIPS) | Lowlight (FID / LPIPS) | Deblur (FID / LPIPS) |\n|---------------|------------------------|---------------------------|------------------------|----------------------|\n| DCP | 92.1 / 0.229 | 95.4 / 0.204| 81.6 / 0.218| 108.2 / 0.231|\n| CycleGAN| 74.5 / 0.146 | 77.9 / 0.167| 70.2 / 0.197| 86.7 / 0.172 |\n| YOLY| 82.7 / 0.198  | 88.3 / 0.202 | 75.4 / 0.210| 98.5 / 0.211|\n| USID-Net| 65.9 / 0.152 | 69.8 / 0.172| 61.7 / 0.188| 76.3 / 0.162|\n| RefineDNet| 54.3 / 0.104| 58.2 / 0.147| 55.8 / 0.179| 68.0 / 0.150|\n| D⁴| 47.9 / 0.098| 52.5 / 0.124| 51.2 / 0.155| 61.2 / 0.139|\n| CUT | 42.1 / 0.111| 46.0 / 0.118| 46.3 / 0.142| 57.9 / 0.143|\n| Santa| 38.3 / 0.096| 42.4 / 0.109 | 41.1 / 0.138| 52.3 / 0.130|\n| UNSB | 31.5 / 0.085 | 35.6 / 0.096| 37.2 / 0.145| 44.9 / 0.126|\n| ODCR | 27.4 / 0.076| 30.9 / 0.091| 33.4 / 0.131 | 40.2 / 0.121|\n| DN | 24.6 / 0.079 | 28.1 / 0.082 | 29.8 / 0.124| 36.9 / 0.118|\n| **DDSB (Ours)** | **23.7 / 0.063** | **26.8 / 0.069**| **27.4 / 0.129** | **31.5 / 0.108**|\n\nShould you have further questions, we are glad to address in the author-reviewer discussion stage."}]

Author rebuttal:

Meta-review: as all the reviewers decide to accept this paper, i recommend to accept this paper. however so many issues are discussed during the rebuttal phase. the authors should revise the paper based on the discussion.
Decision: Accept (poster)