FDG-Diff: Frequency-Domain-Guided Diffusion Framework for Compressed Hazy Image Restoration

Kanghui Tian; Qixiang Liu; Ruicheng Zhang; Zeyu Zhang; Zhi Jin

REVIEW 2 major objections 6 minor 1 cited by

FDG-Diff: Frequency-Domain-Guided Diffusion Framework for Compressed Hazy Image Restoration

T0 review · 2 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper proposes FDG-Diff, a diffusion-based framework that restores JPEG-compressed hazy images by first separating compression loss in the DCT domain, then using that frequency information to guide high-frequency compensation and…

desk verdict A solid, well-engineered entry into a real practical gap—compressed hazy image restoration—but the SOTA claim rests on a comparison against off-the-shelf baselines, so it needs a retrained-baseline check before it is secure. read the letter →

arxiv 2501.12832 v1 pith:AT74ZPOY submitted 2025-01-22 eess.IV cs.CV

Ruicheng Zhang , Kanghui Tian , Zeyu Zhang , Qixiang Liu , Zhi Jin This is my paper · ORCID

classification eess.IVcs.CV

keywords imagedehazingJPEGcompressiondiffusionmodelfrequency-domainguidanceDCTspectrumdecompositionhigh-frequencycompensationdegradation-awaretimesteppredictioncompressedhazyrestoration

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

This paper argues that JPEG compression and haze act jointly, with haze making high-frequency DCT coefficients more likely to be zeroed during quantization. On that basis it proposes FDG-Diff, a diffusion-based dehazing framework that first separates the compression effect from the hazy image in the DCT domain, then uses the predicted compression spectrum to guide high-frequency compensation during reverse sampling. A separate module predicts a per-patch denoising timestep from the transmission map, letting dense-haze regions receive stronger restoration. Across four compressed dehazing benchmarks at quality factor 80, the method reports consistently higher PSNR and SSIM and lower LPIPS and FID than state-of-the-art dehazing models and their cascades with the FBCNN JPEG artifact remover.

What carries the argument

The carrying mechanism is the spectrum decomposition network, which models JPEG compression as a content-independent multiplicative matrix $\varphi$ in the DCT domain ($I_c = \varphi^T I$), then uses log and DCT to turn the product into a sum of a compression-effect spectrum and a lossless hazy-image spectrum. This predicted compression spectrum is the key that unlocks the other two components: the High-Frequency Compensation Module uses Haar-wavelet sampling of skip-connection features and cross-attention against the compression spectrum to add back the high frequencies the quantizer removed, while the Degradation-Aware Denoising Timestep Predictor maps a dark-channel transmission estimate to a per-patch timestep offset, so denser haze gets stronger denoising. The DDPM with these components is trained with an L1 noise-prediction loss and uses overlapping sliding patches with averaged noise estimates to avoid seam artifacts.

What would settle it

Train the spectrum decomposition network on hazy images compressed at QF 10 and compare the predicted compression spectrum against the true rounding residual; if the predicted spectrum correlates with scene content (e.g., contains edges of the hazy scene) rather than only quantizer structure, then the content-independent $\varphi$ assumption fails and the cross-attention guidance is partly using leaked image content. A second check: if removing HFCM or DADTP and simply training the DDPM on corrected hazy images at QF 10 closes the gap to FDG-Diff, then the claimed mechanism is not the driver.

Watch

Extended reading notes

Core claim

The central discovery is that the joint loss from haze and JPEG compression is not merely additive: because haze attenuates AC coefficients before quantization, compressed hazy images lose high-frequency structure far more aggressively than either degradation alone, and this loss is concentrated in dense-haze regions. FDG-Diff exploits this by decomposing the compressed hazy image in the DCT domain into a compression-effect spectrum and a corrected hazy image, with the multiplicative compression model turned additive via a log transform. The corrected image conditions a patch-based DDPM, while the compression spectrum is fed through cross-attention in the High-Frequency Compensation Module to restore wavelet-extracted high-frequency features. The Degradation-Aware Denoising Timestep Predictor adds region-specific denoising intensity. The reported result is consistent state-of-the-art improvement, e.g. NH-Haze at QF 80: PSNR 23.38 dB, SSIM 0.81, LPIPS 0.14, FID 84.65, against 21.78 dB, 0.72, 0.17, 121.06 for the best cascade (FBCNN followed by DehazeDDPM).

Load-bearing premise

The method assumes that JPEG compression acts as a content-independent multiplicative matrix, so after a log transform and DCT the compression effect and the clean hazy image simply add; real JPEG quantization rounds and zeroes coefficients depending on the image content and haze density, so the separation is approximate and the predicted compression spectrum may carry residual scene information.

Editorial extensions

If this is right

Existing dehazing models that ignore compression lose several dB on JPEG inputs, so compression-awareness should be a default consideration for real-world dehazing deployments.
Cascading a JPEG artifact remover before dehazing outperforms the reverse order, but the paper's best cascade still trails FDG-Diff, suggesting that explicit joint modelling beats serial de-artifacting.
The frequency-domain separation idea transfers: any degradation that is approximately multiplicative in a transform domain could be decomposed and used as diffusion guidance.
DADTP's transmission-based timestep prediction gives a general recipe for spatially varying degradations beyond haze, such as non-uniform blur or local compression artifacts.

Reading between the lines

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

Because the paper shows the joint loss grows with haze density, one testable extension is that FDG-Diff's margin over cascades should widen on datasets with denser or more non-uniform haze; the reported Dense-Haze and NH-Haze gains are consistent with that.
The content-independence of $\varphi$ is an idealization; at low quality factors where JPEG rounding and zeroing become highly nonlinear, the predicted compression spectrum may carry residual scene content, so the method's advantage may shrink and a content-dependent correction would be needed.
DADTP is not limited to transmission maps; any regionwise degradation estimate (e.g., local noise variance or blockiness map) could drive timestep offsets in other restoration tasks, suggesting a general region-adaptive diffusion scheduling idea.
The single-channel Y analysis in the problem statement leaves chrominance largely unmodelled; extending the decomposition to the full YUV structure could further improve color fidelity, which the visual results already hint at.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Zhi, if you have to desk-decide this one: it's worth sending out, but the central comparison needs a fix, not the architecture. The paper's real contribution is a new task setting, JPEG-compressed hazy image restoration, and a diffusion model built around it. That gap is genuine: compression is always present in real captures, and existing dehazing methods degrade on compressed inputs. I also think the analysis in Section III is a nice piece of motivation—the inequality that haze increases the probability of quantized AC coefficients going to zero is correct under their stated uniform-transmission simplification, and it does explain why dense haze regions lose high frequency first.

What the paper does well: the spectrum decomposition network is trained directly against paired compressed/uncompressed hazy images, so Equation (10) is just a motivating linear model, not an exact computational requirement. The HFCM and DADTP are plausibly novel, and the ablation shows both contribute something. Results are consistent across four datasets on four metrics, and FID/LPIPS improvements over the higher-quality cascade baselines are sizable. The authors deserve credit for the transparent patch-based fusion formula in Eq. (18) that avoids edge artifacts.

But there are two soft spots. The first is the stress-test issue: Table I compares against baselines, presumably with published weights, while FDG-Diff is trained on the QF-80 compressed training split. No retraining or fine-tuning of baselines is described. That alone could explain a large share of the reported gains. I'd want to see the best cascade baselines (especially FBCNN→DehazeDDPM) retrained or at least fine-tuned on the same compressed training data before believing the SOTA claim. The second is the experimental reporting: no error bars, no multiple seeds, one QF (80), and one train/test split. That's minor in this subfield, but it does cap the confidence of the headline numbers.

The 'first learning-based' claim is probably unverifiable—there is prior learning-based JPEG artifact removal and dehazing, but joint compressed-haze learning may well be new; I'd soften it to 'to our knowledge.' The citation to their own Motion Mamba paper for spectral bias is odd, but not a flaw—Rahaman et al. is also cited.

Bottom line: the method is coherent, the gap is real, and the modules earn their keep in the ablation. This deserves a serious referee, with a request for retrained baselines and error bars. I wouldn't block on the approximation in Eq. (10).

Referee Report

2 major / 6 minor

Summary. The manuscript proposes FDG-Diff, a diffusion-based framework for dehazing JPEG-compressed hazy images. It consists of a DCT-domain spectrum decomposition network that separates a compression-effect spectrum from a corrected hazy image, a High-Frequency Compensation Module (HFCM) that uses wavelet-decomposed features and cross-attention with the compression spectrum, and a Degradation-Aware Denoising Timestep Predictor (DADTP) that adjusts per-patch diffusion timesteps based on a transmission map. Experiments on four hazy-image datasets compressed at QF 80 report consistent improvements over several dehazing baselines and their FBCNN cascades, with a component ablation on NH-Haze. The paper also derives a probabilistic argument that haze increases the chance of JPEG AC-coefficient annihilation.

Significance. The problem addressed is real and underexplored, and the proposed architecture is well motivated by the interaction between haze-induced low contrast and JPEG high-frequency loss. The derivation in Section III is correct under the stated uniform-transmission simplification and gives a concrete reason to expect joint degradation. The component ablation in Table II shows that both HFCM and DADTP contribute, and the paper includes a code link and clear figures. If the reported gains are confirmed under a controlled comparison with baselines trained on the same compressed data, this would be a valuable contribution to practical dehazing. The main risk is evaluation fairness, not the internal consistency of the method.

major comments (2)

[V-A, Table I] Section V-A and Table I: The paper does not state whether any of the neural dehazing baselines or FBCNN cascades were retrained or fine-tuned on the same QF-80 compressed-hazy training split that was used for FDG-Diff. If the baselines are evaluated with published weights, the reported improvements (e.g., NH-Haze PSNR 23.38 dB versus 21.78 dB for FBCNN→DehazeDDPM) could largely reflect in-domain training of the proposed model rather than the HFCM and DADTP components. This is the pivotal control for the central claim; please retrain all deep baselines and cascades under the same training data and protocol, or clearly report and justify any use of off-the-shelf weights.
[V-A, Table I] Section V-A and Table I: Because the last 10% of each dataset is used for testing and the datasets contain only tens of images (I-Haze has about 30, O-Haze 45, Dense-Haze 33, NH-Haze 55), the test sets are likely to contain only 3–5 images. FID is known to be highly unstable at such sample sizes, yet FID is one of the four headline metrics in Table I and drives the claim of consistent perceptual improvement. The reported FID differences (e.g., 84.65 versus 121.06 on NH-Haze) may not be statistically meaningful. Please use a larger test split, report standard deviations or confidence intervals, or replace FID with a more stable distribution-level metric.

minor comments (6)

[IV-A, Eqs. (10)–(12)] The multiplicative matrix model for JPEG compression is not derived from the actual quantization and rounding process; the paper should state explicitly that this is a modeling approximation and that Eq. (12) holds only approximately.
[IV-C, Eq. (18)] It is unclear how patches with different predicted timesteps are trained and how the averaged noise estimate in Eq. (18) is used during sampling; please clarify the training loss for the DADTP and the fusion of overlapping patches with mismatched timesteps.
[III, Eq. (7)] The symbol 'hz(ν)' appears to be a typo for '\hat f^z(ν)', and the sentence containing 'the the probability' should be corrected.
[V-A] The experimental setup reports patch size, stride, and hardware, but not optimizer, learning rate, batch size, or number of training iterations for either network; please include these details or refer to the released code.
[Table II] The ablation is performed only on NH-Haze; given that DADTP is motivated by spatially varying haze, reporting ablations on at least one non-uniform or dense-haze dataset would strengthen the claim.
[V-A, Reference [26]] The choice of QF=80 is justified by an informal web page; please justify it with a more standard source or by a small sensitivity study across quality factors.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: proposed modules are trained on externally generated targets and evaluated on external benchmarks.

full rationale

The paper's derivation chain is self-contained. The spectrum decomposition network is trained with Charbonnier loss against ground-truth compression-effect and clean-hazy DCT spectra (Eq. 13), where those targets are obtained by compressing images from the hazy dataset, not from the model's own output. The DDPM is trained to predict noise on clean-image forward processes conditioned on the corrected hazy image (Eq. 17), so the restoration target is external ground truth. The HFCM and DADTP are learned modules supervised through the same diffusion objective; neither defines success in terms of its own prediction. The only self-citation is [11] (Motion Mamba) in the spectral-bias motivation, but it is paired with the external Rahaman et al. [12] and is not load-bearing for any quantitative claim. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported, and no known result is merely relabeled. The main experimental caveat, whether all baselines were retrained on the same compressed-hazy split before Table I, is a correctness or fairness concern rather than a circularity, because the compared metrics are external and the proposed model's gains could be independently checked. No circular step satisfies the quote-and-reduction requirement.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The theoretical joint-loss claim is parameter-free except for the uniform-transmission simplification, but the practical method introduces several hand-set hyperparameters (patch size, stride, epsilon, QF, unstated timesteps) and one approximate model of JPEG (Equation 10). The method does not postulate new physical or biological entities. The central result therefore rests more on empirical tuning and learned components than on a tight first-principles derivation.

free parameters (5)

Charbonnier loss constant epsilon = 1e-3
Hand-set smoothing constant in Equation (13), used in training the spectrum decomposition network.
Patch size p = 64
Hand-set sliding window patch size for the patch-based diffusion sampling in Section V-A.
Sliding stride r = 16
Hand-set stride for overlapping patch fusion in Section V-A.
JPEG quality factor = QF=80
Single compression level used for all experiments, justified by a blog reference rather than a formal benchmark.
Number of diffusion timesteps T
Needed for training and inference of the DDPM but never specified in the paper, making exact reproduction impossible.

assumptions (6)

domain assumption Atmospheric scattering model (ASM) relates hazy luminance to clean luminance, transmission, and airlight (Equation 1).
Standard model in dehazing, invoked without justification in Section III.
ad hoc to paper Transmission t is uniform within each N x N block (t(m,n) = t in Equation 3).
Used to simplify the DCT derivation and obtain Equation (6); real hazy images have spatially varying transmission, especially in dense or non-homogeneous haze.
ad hoc to paper JPEG compression effect can be represented as a content-independent singular matrix phi with I_c = phi^T I (Equation 10).
This multiplicative separation is an approximation because JPEG quantization involves rounding and content-dependent coefficient zeroing. It is the load-bearing assumption for the spectrum decomposition network.
standard math Logarithmic transformation converts the multiplicative compression model into an additive one, and DCT is linear (Equations 11 and 12).
Standard mathematical properties used to frame the decomposition objective.
domain assumption Deep networks such as U-Net exhibit spectral bias that favors low-frequency learning.
Taken from cited works [11], [12]; used to motivate the need for high-frequency compensation.
domain assumption The dark channel prior transmission map encodes regional haze density and can be used to predict degradation-aware timesteps.
Relies on the validity of the dark channel prior for compressed hazy images, which may be less reliable after JPEG quantization.

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Cite this review

Pith. "Pith review of FDG-Diff: Frequency-Domain-Guided Diffusion Framework for Compressed Hazy Image Restoration." pith.science (2026). https://pith.science/paper/AT74ZPOY

@misc{pith2026250112832,
  author       = {Pith},
  title        = {Pith review of: FDG-Diff: Frequency-Domain-Guided Diffusion Framework for Compressed Hazy Image Restoration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AT74ZPOY}},
  note         = {Machine review of arXiv:2501.12832}
}

read the original abstract

In this study, we reveal that the interaction between haze degradation and JPEG compression introduces complex joint loss effects, which significantly complicate image restoration. Existing dehazing models often neglect compression effects, which limits their effectiveness in practical applications. To address these challenges, we introduce three key contributions. First, we design FDG-Diff, a novel frequency-domain-guided dehazing framework that improves JPEG image restoration by leveraging frequency-domain information. Second, we introduce the High-Frequency Compensation Module (HFCM), which enhances spatial-domain detail restoration by incorporating frequency-domain augmentation techniques into a diffusion-based restoration framework. Lastly, the introduction of the Degradation-Aware Denoising Timestep Predictor (DADTP) module further enhances restoration quality by enabling adaptive region-specific restoration, effectively addressing regional degradation inconsistencies in compressed hazy images. Experimental results across multiple compressed dehazing datasets demonstrate that our method consistently outperforms the latest state-of-the-art approaches. Code be available at https://github.com/SYSUzrc/FDG-Diff.

Figures

Figures reproduced from arXiv: 2501.12832 by the authors.

**Figure 2.** The track of the JPEG process. The colors in the loss map reflect the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** (a) The pipeline of FDG-Diff, comprising a spectrum decomposition network and a compression-aware frequency compensation DDPM. The spectral [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: The structure of DADTAP. The DADTP employs a spatial-channel [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Visual comparison on I-Haze-JPEG [8], O-Haze-JPEG [22], Dense-Haze-JPEG [23], and NH-Haze-JPEG [24], with all inputs compressed at QF 80. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: Ablation study visualizations. Figure (a) illustrates the high-frequency [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

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Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

Single image haze removal using dark channel prior,

Kaiming He et al., “Single image haze removal using dark channel prior,” CVPR, 2009

work page 2009

[2] [2]

Msf 2 dn: Mutil scale feature fusion dehazing network with dense connection,

Guangfa Wang and Xiaokang Yu, “Msf 2 dn: Mutil scale feature fusion dehazing network with dense connection,”

work page

[3] [3]

Vision transformers for single image dehazing,

Yuda Song, Zhuqing He, Hui Qian, and Xin Du, “Vision transformers for single image dehazing,” IEEE Transactions on Image Processing , vol. 32, pp. 1927–1941, 2023

work page 1927

[4] [4]

Image dehazing transformer with transmission-aware 3d position embedding,

Chunle Guo et al., “Image dehazing transformer with transmission-aware 3d position embedding,” in 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 2022, pp. 5802–5810

work page 2022

[5] [5]

Frequency compensated diffusion model for real-scene dehazing,

Jing Wang, Songtao Wu, Zhiqiang Yuan, Qiang Tong, and Kuanhong Xu, “Frequency compensated diffusion model for real-scene dehazing,” Neural Networks, 2024

work page 2024

[6] [6]

Ffa-net: Feature fusion attention network for single image dehazing,

Xu Qin, Zhilin Wang, Yuanchao Bai, Xiaodong Xie, and Huizhu Jia, “Ffa-net: Feature fusion attention network for single image dehazing,” in National Conference on Artificial Intelligence(AAAI) , 2020

work page 2020

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High-quality image dehazing with diffusion model,

Hu Yu, Jie Huang, Kaiwen Zheng, and Feng Zhao, “High-quality image dehazing with diffusion model,” 2024

work page 2024

[8] [8]

I-haze: A dehazing benchmark with real hazy and haze-free indoor images,

C. Ancuti, C. O. Ancuti, R. Timofte, and C. De Vleeschouwer, “I-haze: A dehazing benchmark with real hazy and haze-free indoor images,” in Advanced Concepts for IntelliC.gent Vision Systems. 2018, pp. 620–631, Springer

work page 2018