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REVIEW 4 major objections 5 minor 51 references

When Schr\"odinger Bridge Meets Real-World Image Dehazing with Unpaired Training

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that modeling unpaired image dehazing as a Schrödinger Bridge—an entropy-regularized optimal transport path between hazy and clear image distributions—produces state-of-the-art dehazing results in just a few sampling…

desk verdict A solid unpaired dehazing system with plausible metrics, but the OT theory is asserted rather than shown and a key baseline is missing—worth refereeing with requests for the supplement and a fairer comparison set. read the letter →

arxiv 2507.09524 v1 pith:PVDVJLSR submitted 2025-07-13 cs.CV

Yunwei Lan , Zhigao Cui , Xin Luo , Chang Liu , Nian Wang , Menglin Zhang , Yanzhao Su , Dong Liu This is my paper
classification cs.CV
keywords SchrödingerbridgeunpairedimagedehazingoptimaltransportCLIPpromptlearningdetail-preservingregularizationreal-worldimage-to-imagetranslation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper introduces DehazeSB, an unpaired dehazing framework that treats restoration as a Schrödinger Bridge problem: instead of a single GAN mapping or a diffusion loop through Gaussian noise, it learns a near-optimal stochastic transport path from the distribution of hazy images to the distribution of clear images. The central claim is that this optimal-transport mapping delivers high-quality dehazed images in a few function evaluations and outperforms prior dehazing methods on real-world benchmarks, including methods trained with paired data. Two auxiliary components carry much of the practical performance: a learned haze-aware text prompt that steers a pre-trained vision-language model to separate hazy from clear images, and detail-preserving regularization that keeps structure and texture aligned. A sympathetic reader would summarize the paper's bet as: the right transport model can close the gap between unpaired and paired dehazing.

What carries the argument

The machinery is the static Schrödinger Bridge, formulated as an entropy-regularized optimal transport problem between the hazy distribution $\pi_0$ and the clear distribution $\pi_1$: $Q_{01}^{\mathrm{SB}} = \arg\min_{\gamma \in \Pi(\pi_0,\pi_1)} \mathbb{E}_{(x_0,x_1)\sim\gamma}\|x_0-x_1\|^2 - 2\tau H(\gamma)$. Its key property is that intermediate states follow conditional Gaussians, $p(x(t)\mid x_0,x_1) = \mathcal{N}(tx_1 + (1-t)x_0,\; t(1-t)\tau I)$, and the bridge's self-similarity lets any sub-interval be interpolated recursively. The paper discretizes $[0,1]$ into $N=5$ intervals and trains one time-conditioned generator $G: q_\theta(x_1\mid x(t_i))$ that predicts the target from any intermediate state, using Eq. (12) to step through intermediate states. The load-bearing identity is the reduction of the KL-constrained bridge objective to the weighted loss $L = L_{\mathrm{adv}} + \lambda_{\mathrm{SB}} L_{\mathrm{SB}}$ via Lagrange multipliers, with the entropy term $H(q_\theta(x(t_i),x_1))$ computed as in the paper's reference [20].

What would settle it

Take the released code and retrain on the same unpaired sets with the term $H(q_\theta(x(t_i),x_1))$ replaced by a constant or removed while keeping all other losses; if the RTTS FID stays near the reported 53.120, the Schrödinger Bridge term is not the performance driver. Independently, the derivation from Eq. (3) to Eq. (10) is compressed into 'Using Lagrange multipliers' and the entropy computation is deferred to a supplementary file not present in this preprint, so a full re-derivation that exposes a missing constraint would falsify the theoretical claim even if the output images remain plausible.

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Extended reading notes

Core claim

The core claim is that a Schrödinger Bridge objective, implemented with a single time-conditioned generator and an adversarial loss, can replace both the limited mapping of GAN generators and the many-step Gaussian-noise diffusion pipeline for unpaired dehazing. Concretely, the paper optimizes $L = L_{\mathrm{adv}} + \lambda_{\mathrm{SB}} L_{\mathrm{SB}}$ plus regularization terms, where $L_{\mathrm{SB}}$ is the entropy-regularized transport cost between intermediate states $x(t_i)$ and the target $x_1$, and reports that this yields optimal transport from hazy to clear images in fewer steps. On RTTS and Haze2020 it reports the best FID among all compared methods (53.120 and 69.796, respectively), and on OHAZE it reports the best full-reference scores (PSNR 18.829, SSIM 0.838), beating paired-training baselines. It also claims the learned haze-aware prompt outperforms fixed prompts such as "hazy image" at distinguishing hazy from clear, with ablations attributing gains to prompt learning and to the physical-prior and high-frequency regularizations.

Load-bearing premise

The load-bearing premise is that one shared time-conditioned generator, trained with the adversarial loss plus the entropy-regularized transport objective with the entropy computed in the style of reference [20], truly realizes the Schrödinger Bridge transition between hazy and clear distributions; if that objective is not what the training actually implements, the claimed optimal-transport advantage is unsupported.

Editorial extensions

If this is right

  • If the central claim holds, unpaired dehazing trained on real-world hazy photos can match or beat paired synthetic-trained models on real benchmarks, easing the data bottleneck.
  • The adjustable number of function evaluations, down to one step, makes the approach more practical for deployment than diffusion-based dehazing pipelines.
  • The learned haze-aware prompt offers a reusable way to inject vision-language knowledge into low-level restoration without paired data.
  • The ablations show that the detail-preserving regularizers each contribute, so the recipe is transferable to other unpaired restoration frameworks.
  • The reported generalization across RTTS, Haze2020, OHAZE, and IHAZE without retraining suggests the transport captures a domain-level correspondence rather than dataset-specific artifacts.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: the same Schrödinger Bridge formulation is task-agnostic, so a natural testable extension is to apply the identical loss to other unpaired restorations such as low-light enhancement, deraining, or super-resolution, and compare against task-specific GAN baselines; the paper does not make this claim.
  • Editorial inference: the derivation from Eq. (3) to Eq. (10) is compressed into "Using Lagrange multipliers," and the entropy computation is deferred to a supplementary file that is not present in this preprint, so an independent re-derivation and an open-sourced entropy implementation would settle whether the SB objective, rather than the adversarial and regularization terms, drives the reported
  • Editorial inference: the learned prompt is a single global vector, so extending it to per-image or per-patch adaptive prompts could improve robustness to the varying haze densities the paper acknowledges as a limitation, and would be a natural next experiment.
  • Editorial inference: because OHAZE and IHAZE have ground truth and DehazeSB was not retrained on them, a direct comparison with the same model fine-tuned on those paired sets would separate the benefit of the transport prior from the benefit of seeing target-domain data.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes DehazeSB, an unpaired image dehazing framework built on a Schrödinger Bridge formulation. The method first learns a haze-aware CLIP text prompt, then trains a time-conditioned generator with adversarial and SB losses, and adds detail-preserving regularization that combines PatchNCE, physical prior, and high-frequency losses. The authors claim state-of-the-art performance on RTTS, Haze2020, OHAZE, and IHAZE with fewer function evaluations than diffusion baselines, and they provide a public code repository. The manuscript includes quantitative and qualitative comparisons, plus ablations of prompt learning and detail-preservation components.

Significance. If the central theoretical derivation were made rigorous, DehazeSB would be a meaningful advance: it applies entropy-regularized optimal transport/Schrödinger Bridge ideas to unpaired real-world dehazing, combines them with adversarial training and CLIP prompt learning, and reports strong no-reference metrics on several benchmarks. Strengths of the paper include a released codebase, training on real unpaired hazy and clear images, and component-wise ablation studies. However, the main theoretical claim is currently not verifiable because the SB loss derivation and the entropy computation are deferred to an absent supplement, and the empirical SOTA claim omits the most relevant baseline. The work is potentially significant, but it requires substantive revision before the claims can be relied upon.

major comments (4)
  1. [§4.2, Eq. (10)-(12)] The central loss is asserted rather than derived. Eq. (10) is introduced as the definition of LSB, and Eq. (11) is said to follow "Using Lagrange multipliers," but no derivation connects the static SB problem in Eq. (3) to this objective. In particular, the conditions under which the Markov-chain marginals generated by Eq. (12) match the SB interpolant, the equivalence between H(qθ(x(ti),x1)) and the entropy term in Eq. (3) (including the (1−ti) factor), and the validity of a single time-conditioned generator with an adversarial constraint are all assumed. The text states that the entropy is computed "in a manner similar to UNSB, as detailed in our supplementary materials," but the supplementary file is not present in the preprint. Because the abstract's claim of optimal transport mappings from hazy to clear images rests on Eq. (10), this derivation and the entropy computation must be supplied in the main text or in an accessible supplement before the theoretical claim can be evaluated.
  2. [Tables 1-2] The most relevant baseline, the authors' own unpaired diffusion dehazing method [22], is omitted from both quantitative tables. Since [22] is also an unpaired diffusion-based dehazer, its absence is particularly damaging to the abstract's claim that DehazeSB surpasses existing state-of-the-art dehazing methods, including unpaired ones. Please add [22] and any other recent unpaired diffusion dehazing baselines to Tables 1 and 2 and discuss the comparison, including the number of function evaluations.
  3. [Tables 1-4] No experiment is repeated, and no standard deviation or confidence interval is reported. Several of the reported differences are small (e.g., NIQE 3.743 vs. 3.712 in Table 3, or FID 69.796 vs. 72.812 in Table 1), so without variance estimates it is impossible to assess whether these differences are statistically meaningful. At minimum, report the mean and standard deviation over at least three training runs with different seeds for the main tables and the ablation study.
  4. [§4.3.2, Eq. (13)] The physical prior loss Lphy = Lrec(I, Iphy) with Iphy = J tref + A(1−tref) admits a trivial solution in which J ≈ I and tref ≈ 1, reconstructing the hazy input exactly. The adversarial and SB losses may prevent full collapse, but no analysis or ablation isolates this degeneracy. Please provide evidence that the refined transmission map is non-trivial (e.g., visualizations or statistics of tref) and show that removing Lphy does not trade off identity preservation against actual dehazing.
minor comments (5)
  1. [§5] The section title "Exprements and Discussion" contains a typo; it should read "Experiments."
  2. [Table 1] The row labeled "Unpaired UNSB [8]" appears to cite [8] (CUNSB-RFIE) for UNSB, whereas UNSB is reference [20]; please correct the citation and ensure that the baseline is the actual UNSB method.
  3. [§5.2, Table 2] The text says Table 2 presents results on OHAZE and IHAZE, but the table only reports OHAZE; the IHAZE results are presumably in the missing supplementary material and should be explicitly stated as such.
  4. [Equations (7) and (8)] The softmax-like expressions in Eqs. (7) and (8) have formatting issues, and the role of the label y in the BCE loss could be clarified in prose to make clear which class is positive and which is negative.
  5. [General] The supplementary materials are referenced in §4.2, §4.3.1, §4.3.3, and §5, but they are not available in the preprint. All referenced implementation details, entropy computations, and additional results should be made publicly accessible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Schrödinger Bridge objective is imported from external UNSB/I2SB work, the CLIP prompt is learned from data, and no prediction reduces to a fitted parameter by construction.

full rationale

The claimed derivation chain is not circular. Equation (3) is the standard static Schrödinger Bridge entropy-regularized optimal transport problem, taken from the external UNSB and I2SB literature; the paper does not define the hazy or clear distributions in terms of its own dehazing loss. The transition to Eq. (10) follows UNSB's generator parameterization q_theta(x1 | x(ti)), and the paper explicitly says the entropy term is computed "in a manner similar to UNSB," an external, code-released method, not the authors' own theorem. The CLIP prompt is optimized from unpaired data with a binary cross-entropy objective, so the discriminator signal is not a renamed output of the dehazing network. The detail-preserving regularizers (PatchNCE, DCP-based physical prior, DFT/SSIM/Sobel) are standard externally introduced losses. None of the reported metrics are fitted parameters of the model; they are evaluated on held-out RTTS, Haze2020, OHAZE, and IHAZE datasets. The single self-citation [22] (Lan et al., AAAI 2025) appears in a list of prior unpaired dehazing methods and is not load-bearing for the SB derivation. The paper does omit the derivation from Eq. (3) to Eq. (10) and defers the entropy computation to an absent supplementary file; this is an exposition and completeness problem, not a case of a prediction being equivalent to its input by construction. The table label "UNSB [8]" also mismatches the reference list, which is a correctness risk rather than circularity. Overall, the central claim is externally anchored and self-contained against benchmarks, so the circularity score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central claim rests on the UNSB-derived SB formulation, the ASM degradation model, and the reliability of DCP and CLIP for real-world haze. The main free parameters are loss weights, interval count, and entropy coefficient, none of which are given sensitivity analysis in the main text.

free parameters (3)
  • Loss weights lambda_SB, lambda_p, lambda_NCE, lambda_phy, lambda_hfd = 1, 1, 1, 0.5, 0.5
    Hand-chosen coefficients in Eq. 14; no sensitivity analysis reported in the main text.
  • Number of SB intervals N = 5
    Selected for discretizing [0,1] in Section 4.2; ablation of interval count is deferred to a missing supplement.
  • Entropy regularization coefficient tau = Not reported in main text
    Appears in Eqs. 3, 5, 10, and 12; controls trajectory randomness; no value given in the visible text.
assumptions (5)
  • domain assumption Atmospheric Scattering Model (ASM) I = J t + A(1-t) accurately describes real hazy image formation.
    Invoked in Eq. 1 and used in the physical prior regularization (Sec 4.3.2) to reconstruct the hazy image; if ASM is violated, the regularization is mis-specified.
  • domain assumption Dark Channel Prior (DCP) estimates of atmospheric light A and transmission t are reliable enough for real-world hazy images.
    Sec 4.3.2 uses DCP to obtain A, t, and J_dcp; DCP is known to fail on bright sky regions and on scenes with large bright areas.
  • domain assumption Pre-trained CLIP embeddings can separate hazy from clear images at the image level.
    Sec 4.1 relies on this for the prompt learning and for the CLIP-based discriminator; Figure 3 shows support but with a limited demonstration.
  • standard math The Schrödinger Bridge self-similarity property (Eq. 5) holds for the learned process, as proven in UNSB [20].
    Used to derive the recursive interpolation in Eq. 12; accepted from the cited UNSB paper without re-derivation.
  • standard math The static SB formulation (Eq. 3) is equivalent to the entropy-regularized optimal transport problem with Gaussian conditional marginals (Eq. 4).
    Background from SB theory, cited to [20,27]; not re-derived here.
invented entities (1)
  • Haze-aware textual prompt T_hazy independent evidence
    purpose: Provides a learned CLIP text embedding that distinguishes hazy from clear images and guides the Schrödinger Bridge generator to push dehazed outputs away from the hazy description.
    The prompt is trained with a BCE loss and validated in ablations (Table 3) and in the CLIP score visualization (Figure 3), giving a falsifiable handle through classification accuracy and downstream quality metrics.

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Cite this review

Pith. "Pith review of When Schr\"odinger Bridge Meets Real-World Image Dehazing with Unpaired Training." pith.science (2026). https://pith.science/paper/PVDVJLSR

@misc{pith2026250709524,
  author       = {Pith},
  title        = {Pith review of: When Schr\"odinger Bridge Meets Real-World Image Dehazing with Unpaired Training},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PVDVJLSR}},
  note         = {Machine review of arXiv:2507.09524}
}
read the original abstract

Recent advancements in unpaired dehazing, particularly those using GANs, show promising performance in processing real-world hazy images. However, these methods tend to face limitations due to the generator's limited transport mapping capability, which hinders the full exploitation of their effectiveness in unpaired training paradigms. To address these challenges, we propose DehazeSB, a novel unpaired dehazing framework based on the Schr\"odinger Bridge. By leveraging optimal transport (OT) theory, DehazeSB directly bridges the distributions between hazy and clear images. This enables optimal transport mappings from hazy to clear images in fewer steps, thereby generating high-quality results. To ensure the consistency of structural information and details in the restored images, we introduce detail-preserving regularization, which enforces pixel-level alignment between hazy inputs and dehazed outputs. Furthermore, we propose a novel prompt learning to leverage pre-trained CLIP models in distinguishing hazy images and clear ones, by learning a haze-aware vision-language alignment. Extensive experiments on multiple real-world datasets demonstrate our method's superiority. Code: https://github.com/ywxjm/DehazeSB.

Figures

Figures reproduced from arXiv: 2507.09524 by the authors.

Figure 1
Figure 1. Existing GAN-based unpaired dehazing methods struggle to handle images with complex structures due to the lim￾ited mapping capability of the generator. While diffusion model￾based methods can achieve more intricate transport mappings, they necessitate transforming images into Gaussian noise and then regenerating them through a large number of sampling steps. Our Schrodinger Bridge ¨ enables the direct learning of op… view at source ↗
Figure 2
Figure 2. Overview of our method. We first learn a haze-aware prompt using prompt learning. This learned prompt is then used to guide [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. CLIP scores of different prompts. We observe that [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Visual comparison of samples from RTTS and Haze2020. Our method can effectively remove haze and generate high-quality [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Visual comparison of samples from OHAZE and IHAZE. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Ablation study of each component. (a) Hazy image. (b) [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.