Luminance-Aware Statistical Quantization: Unsupervised Hierarchical Learning for Illumination Enhancement

We sincerely thank the reviewer for their valuable feedback and for giving us the opportunity to further explain and improve our work. We address each of your comments in detail below, and we hope that our responses resolve any questions or concerns you may have.

Q1: Robustness Beyond the Power-Law Assumption

We would like to clarify that our approach employs a coarse-to-fine MCMC sampling strategy to fit the luminance adaptation space, rather than rigidly enforcing the power-law assumption. As discussed in Appendix A (paragraph 4), we reinterpret the strict power-law model as a relaxed prior and leverage MCMC sampling—integrated with the forward process of a diffusion model—to explore the distribution space.

This design enables LASQ to flexibly capture a wider family of luminance mappings that are only loosely guided by the physics-inspired prior, rather than being constrained to a fixed analytical form. As a result, our method does not critically depend on the power-law assumption itself. The MCMC-based inference operates at a structured level, incorporating spatial context, which allows it to remain robust under spatially inconsistent or extreme lighting conditions—well beyond the capabilities of per-pixel or strictly model-driven approaches.

Challenging scenarios such as extreme dynamic range and heavy sensor noise, as you mentioned, will be specifically evaluated in the following rebuttal. The corresponding quantitative results further demonstrate the robustness of LASQ under these conditions.

Q2 & W2, W4: Hyperparameter Selection and Ablation

We conducted a hyperparameter sensitivity analysis on the LSRW dataset :

We varied key hyperparameters ($\beta_{p}$ is determined by $\eta$ and $\delta$, where $\delta$ is a variance stabilization factor typically set to 0.001) over a range. Results show only moderate metric changes. For example, $\alpha$ from 0.05 to 0.6 alters PSNR by <0.3 dB, with minimal perceptual impact. Performance improves with larger $N$ but saturates beyond $N{=}100$, which we adopt as the default for a quality-efficiency trade-off. Results show our method is robust and stable across a wide hyperparameter range, indicating strong generalization.

We also conducted more ablation studies using both LSRW and LMIE:

We performed ablation studies to evaluate key components of LASQ. The case of $k=0$, corresponding to enhancement in pixel space, yields the weakest results—validating the effectiveness of our latent-space design. Additionally, removing $\mathcal{L}_{\text{g}}$ leads to clear performance drops, confirming its importance to the final quality.

Q3: Effectiveness of the Adversarial Head in Unpaired Settings

We would like to clarify that the introduced adversarial discriminator is applied to unpaired references. In fact, the LASQ++ variant in our main paper is trained strictly with unpaired references, and the adversarial head still provides clear improvements in texture fidelity under this setting. We will revise the manuscript to better emphasize this point and avoid possible misunderstandings. Importantly, the adversarial discriminator does not introduce any instability during optimization, thanks to the appropriate choice of the weighting parameter $\lambda_{GAN}$. The detailed performance metrics are provided below.

Q4: Generalization Limits and Adaptive Strategies on LOL Dataset

LASQ has demonstrated strong generalization ability and stability, surpassing some supervised methods on datasets such as LSWR, DICM, NPE, and VV. However, in the LOL dataset, where the training and testing images often come from similar scenes, supervised paired-learning methods can better fit the overall data distribution. Since LASQ does not utilize any reference images during training, its performance on certain metrics may be lower than that of supervised approaches. We analyzed the error maps and found that the primary issues are concentrated in a few images, where LASQ tends to produce less detailed textures and shows a global luminance discrepancy compared to the ground truth.

As a diffusion-based generative model, LASQ may occasionally generate overly smooth results. To address this, we plan to improve the decoder’s sensitivity to fine details by incorporating multi-scale texture refinement modules. Additionally, we will introduce a structure-aware loss function designed to explicitly penalize over-smoothing in regions with high structural complexity.

Furthermore, since LASQ operates without any reference images, it may lack awareness of the specific luminance distribution present in the LOL dataset. To mitigate this, we propose to anchor the MCMC sampling process around the dataset's typical luminance domain, using it as a prior to better align the generated outputs with the illumination characteristics of LOL images.

Q5 & W2, W3: Evaluation Analysis under Challenging Conditions

We first evaluated LASQ on “raw images” captured by three “different camera” models in the ELD dataset. The results show that LASQ achieves consistently strong performance across all camera sources, suggesting that our approach is not sensitive to differences in camera hardware or imaging pipelines. In contrast, other methods exhibit significantly less stability.

To further examine robustness under challenging conditions, we applied LASQ to three representative datasets: ELD, which contains “raw sensor data” captured under “extreme dynamic lighting”; LOL_blur, which includes low-light images degraded by “motion blur”; and LED, which comprises low-light images affected by “LED flicker”.

Although performance metrics are slightly reduced compared to standard scenes, LASQ still achieves the best results across all three challenging conditions. This highlights its robustness and adaptability to real-world failure modes. In particular, the relatively strong performance under motion blur and LED flicker suggests that the proposed physics-aware design helps mitigate degradation caused by non-ideal sensor inputs and dynamic lighting effects, without relying on explicit temporal modeling or post-processing.

Under extreme conditions—such as low illumination or severe motion blur—our original framework showed limitations in preserving fine textures and accurate brightness. We will explore enhancing the decoder with multi-scale texture refinement and anchoring the MCMC sampling distribution to the ground truth luminance characteristics observed in extreme cases.

W4: Inference Computation

We compare LASQ with early lightweight methods (e.g., EnlightenGAN, KinD++) and recent diffusion models (e.g., WCDM, LightenDiffusion). While diffusion models outperform early methods, they are computationally heavy. LASQ retains their performance but offers much higher efficiency without relying on reference images, making its moderate overhead a practical trade-off.

All supplementary tables and visualizations will be included in the final version of the paper or appendix.

We sincerely thank you for your valuable feedback and constructive suggestions. We are particularly encouraged by your recognition of LASQ as "a novel, physics-inspired framework". Below, we provide a point-by-point response to your comments.

Q1: Learnable Fusion Weights via HMM-Based Adaptation

Thank you for your insightful suggestion — it aligns well with our own research perspective. We further explore an HMM-based auto-tuning framework that dynamically updates both the network hyperparameters and the fusion weights on a per-batch basis.

We begin by randomly initializing the hierarchical weights $W=\\{w_1, w_2,...,w_n\\}$ for coarse-to-fine feature fusion. At each timestep $t$, the emission probability is defined as:

$p(\mathcal{F}^{t}\_{H}|{\Theta}^{t}) = p(\mathcal{F}^{t}\_{H}|{\theta}^{t}\_\text{diff},W,\mathcal{I}\_{H}^t)p(\mathcal{I}\_{H}^t|\gamma)p(\gamma|\theta^{t}\_\text{hyper})$

Here, the hidden states $\Theta^t$ include diffusion model parameters, hyperparameters and hierarchical fusion weights ($\Theta^t=\\{{\theta}^{t}\_\text{diff},\theta^{t}\_\text{hyper},W\\}$), while $\gamma$ is drawn from a hyperparameter-dependent distribution. The term $p(\mathcal{I}_H^t|\gamma)$ models MCMC-based sampling, and $p(\mathcal{F}_H^t|\cdot)$ corresponds to the actual diffusion output conditioned on the intermediate latent representation. The state transition follows:

$p({\Theta}^{t+1}|{\Theta}^{t},\mathcal{F}^{t}\_{H}) = p({\Theta}^{t+1}|{\Theta}^{t},\mathcal{L}\_{\text{total}}^{t})p(\mathcal{L}\_{\text{total}}^{t}|\mathcal{F}^{t}\_{H})$

This framework enables the model to adaptively assign importance to hierarchical levels based on data distribution, thereby enhancing fusion effectiveness and mitigating risks such as overfitting or suboptimal manual tuning. We will include this auto-tuning strategy as an extension in the revised version to demonstrate its feasibility and performance impact.

Q2: Necessity and Efficiency of Diffusion-Based Fusion

In LASQ, the luminance adaptation space is explored through a progressive MCMC sampling strategy, embedded with the forward process of a diffusion model. Specifically, the sampling over luminance states at different noise levels $t$ is aligned with the trajectory of the diffusion process, enabling structured and gradual adaptation of luminance features. This integration allows for effective exploration of the latent luminance space without requiring heavy supervision or fine-tuning, while ensuring stable convergence across diverse lighting conditions.

The diffusion model enables unsupervised traversal across hierarchical luminance layers, and provides a principled mechanism to progressively refine luminance representations from coarse global estimates to fine local details. This aligns well with the hierarchical structure of luminance variations in natural scenes, and allows the model to adaptively balance global consistency and local contrast. This layer-wise sampling and fusion strategy enhances the model’s robustness to complex illumination patterns and supports high generalization under diverse low-light conditions, without any reference images.

We appreciate the suggestion to explore more lightweight alternatives. We will explore adapting LASQ to lightweight models (e.g., CNNs) via a hierarchical luminance-based data augmentation strategy. Specifically, the augmented luminance maps will be allocated to different layers of the CNN, enabling image enhancement through a hierarchical training strategy. This framework maintains the core principle of hierarchical adaptation while significantly reducing computational overhead—all without requiring access to reference images. We consider this a promising direction for future research.

Q3 & W1: Computational Cost

We have now added detailed computational complexity metrics below (NVIDIA A800, LOL dataset). We clarify that the coarse-to-fine MCMC sampling mechanism is only used during training and is embedded into the forward diffusion process. It guides the model to traverse luminance layers in a hierarchical manner, enabling structured learning of light propagation. During inference, our model only performs the denoising step conditioned on the low-light input within the diffusion model, which is significantly more efficient.

We compare LASQ against both early non-diffusion-based methods (e.g., EnlightenGAN, KinD++), and recent diffusion-based approaches (e.g., WCDM, LightenDiffusion). While the early methods are lightweight, their performance lags far behind diffusion-based models across all key metrics. Existing diffusion models, although significantly more effective, tend to suffer from high computational cost due to deep architectures and iterative sampling. LASQ, while maintaining the performance advantages of diffusion models, achieves inference efficiency comparable to non-diffusion-based methods. Considering the substantial performance gain without reliance on reference images, the moderate computational overhead of LASQ is a practical and acceptable trade-off. Therefore, LASQ strikes a favorable balance between performance and computational efficiency, enabling deployment on low-power devices equipped with less than 8GB of GPU memory (e.g., NVIDIA Jetson AGX Orin), without compromising image enhancement quality. In future work, we also plan to explore lightweight variants of our framework for further efficiency.

Q4: Texture Preservation in Diffusion-Based Enhancement

Thank you for pointing this issue. As a diffusion-based generative model, LASQ may, in some isolated cases, produce overly smooth results with less detailed texture, particularly under challenging lighting or structure-less regions. However, on the full LSRW test set, LASQ outperforms both NeRCo and PairLIE in terms of all major evaluation metrics, indicating overall superior perceptual quality. Moreover, such texture-smoothing artifacts occur in less than 10% of the test cases.

To mitigate this issue in future work, we plan to enhance the decoder's detail sensitivity through multi-scale texture refinement modules, and introduce a structure-aware loss function that explicitly penalizes over-smoothing in texture-rich regions.

W2: Hyperparameter Selection and Sensitivity

We conducted a hyperparameter sensitivity analysis on the LSRW dataset :

We varied key hyperparameters ($\beta_p$ is derived from $\eta$) over a range. Results show only moderate metric changes. For example, $\alpha$ from 0.05 to 0.6 alters PSNR by <0.3 dB, with minimal perceptual impact. Other hyperparameters show similar stability, indicating strong robustness to tuning. We also evaluated two structural parameters on both LSRW and LMIE:

Performance improves with larger $k$ and $N$, but saturates beyond $k{=}3$ and $N{=}100$; we adopt these as defaults for a quality-efficiency trade-off. Results show our method is robust and stable across a wide hyperparameter range, indicating strong generalization.

All supplementary tables and visualizations will be included in the final version of the paper or appendix.

We sincerely thank the reviewer for identifying several important concerns and for the opportunity to further clarify our method. We address each point in detail below.

Q1 & W3: Hyperparameter Selection and Sensitivity

We conducted a hyperparameter sensitivity analysis on the LSRW dataset :

We varied key hyperparameters ($\beta_p$ is derived from $\eta$) over a range. Results show only moderate metric changes. For example, $\alpha$ from 0.05 to 0.6 alters PSNR by <0.3 dB, with minimal perceptual impact. Other hyperparameters show similar stability, indicating strong robustness to tuning. We also evaluated two structural parameters on both LSRW and LMIE:

Performance improves with larger $k$ and $N$, but saturates beyond $k{=}3$ and $N{=}100$; we adopt these as defaults for a quality-efficiency trade-off. Results show our method is robust and stable across a wide hyperparameter range, indicating strong generalization.

In addition to the datasets reported in the main text (LOL, LSRW, DICM, NPE, VV, LIME, MEF), we tested LASQ on several challenging unseen domains—LOL_blur, LED, ELD, and Light-Effects—using the same fixed hyperparameters. Due to space constraints, detailed results are shown in the responses to the other reviewers. Consistently strong performance in these scenarios further confirms that LASQ generalizes well across diverse domains without retraining or re-tuning.

To improve generalization to new datasets, we add a hyperparameter summary table in the appendix. While tuning often generalizes well, we further explore an hidden Markov model (HMM)-based auto-tuning framework that updates both network and hyperparameters per batch. Specifically, the emission probability is:

$p(\mathcal{F}^{t}\_{H}|{\Theta}^{t}) = p(\mathcal{F}^{t}\_{H}|{\theta}^{t}\_\text{diff},\mathcal{I}\_{H}^t)p(\mathcal{I}\_{H}^t|\gamma)p(\gamma|\theta^{t}\_\text{hyper})$

where hidden states $\Theta^t=\\{{\theta}^{t}\_\text{diff},\theta^{t}\_\text{hyper}\\}$. $\gamma$ is drawn from a hyperparameter-dependent distribution. $p(\mathcal{I}_H^t|\gamma)$ models MCMC sampling, and $p(\mathcal{F}_H^t|\cdot)$ corresponds to the diffusion process. The state transition follows:

$p({\Theta}^{t+1}|{\Theta}^{t},\mathcal{F}^{t}\_{H}) = p({\Theta}^{t+1}|{\Theta}^{t},\mathcal{L}\_{\text{total}}^{t})p(\mathcal{L}\_{\text{total}}^{t}|\mathcal{F}^{t}\_{H})$

This captures Bayesian updates of parameters. For gradient-based hyperparameter updates, we apply the chain rule:

$\frac{\partial \mathcal{L}\_{\text{total}}^t}{\partial \theta^t\_{\text{hyper}}} = \mathbb{E}\_{\gamma \sim p(\gamma \mid \theta^t\_{\text{hyper}})} \left[ \frac{\partial \mathcal{L}\_{\text{total}}^t}{\partial \mathcal{F}\_H^t} \cdot \frac{\partial \mathcal{F}\_H^t}{\partial \gamma} \cdot \frac{\partial \gamma}{\partial \theta^t\_{\text{hyper}}} \right]$

This framework reduces manual tuning and mitigates overfitting by dynamically adapting to data distributions. Preliminary experiments on the LSRW dataset show about 6% performance improvement.

Q2 & W2: Clarification on MCMC Sampling Cost and Convergence

We have now added detailed computational complexity metrics below (NVIDIA A800, LOL dataset). We clarify that the coarse-to-fine MCMC sampling mechanism is only used during training and is embedded into the forward diffusion process. It guides the model to traverse luminance layers in a hierarchical manner, enabling structured learning of light propagation. During inference, our model only performs the denoising step conditioned on the low-light input within the diffusion model, which is significantly more efficient.

We compare LASQ against both early non-diffusion-based methods (e.g., EnlightenGAN, KinD++), and recent diffusion-based approaches (e.g., WCDM, LightenDiffusion). While the early methods are lightweight, their performance lags far behind diffusion-based models across all key metrics. Existing diffusion models, although significantly more effective, tend to suffer from high computational cost due to deep architectures and iterative sampling. LASQ, while maintaining the performance advantages of diffusion models, achieves inference efficiency comparable to non-diffusion-based methods. This makes it highly suitable for real-world deployment. Considering the substantial performance gain without reliance on reference images, the moderate computational overhead of LASQ is a practical and acceptable trade-off. In future work, we also plan to explore lightweight variants of our framework for further efficiency.

While we reiterate that MCMC sampling is only applied during training, we fully acknowledge the importance of convergence efficiency and training stability. Notably, the sampling process is embedded into the forward diffusion trajectory, inherently generating a large number of diverse samples throughout training. This ensures thorough exploration of the latent space. Furthermore, the structured design of the latent operator space, the coarse-to-fine hierarchical sampling strategy, and the learned Markov regularization collectively facilitate natural and stable convergence without the need for excessive iterations.

Q3 & W1: Clarification on "Instability in Low-Intensity Areas"

We would like to clarify that our approach employs a coarse-to-fine MCMC sampling strategy to fit the luminance adaptation space, rather than rigidly enforcing the power-law assumption. As discussed in Appendix A (paragraph 4), we reinterpret the strict power-law model as a relaxed prior and leverage MCMC sampling—integrated with the forward process of a diffusion model—to explore the distribution space.

This design enables LASQ to flexibly capture a wider family of luminance mappings that are only loosely guided by the physics-inspired prior, rather than being constrained to a fixed analytical form. As a result, our method does not critically depend on the power-law assumption itself. The MCMC-based inference operates at a structured level, incorporating spatial context, which allows it to remain robust under spatially inconsistent or extreme lighting conditions—well beyond the capabilities of per-pixel or strictly model-driven approaches.

To further support this claim, we conduct comparative evaluations on the ELD dataset, which contains extremely low-light scenarios with strong noise and minimal luminance signal. As shown below, LASQ achieves competitive performance compared to prior methods, demonstrating its robustness even under severe low-intensity degradations. Its strong performance in additional challenging conditions—such as motion blur, extreme dynamic range, and LED flicker—is presented in our responses to other reviewers, further highlighting the stability and generalizability of LASQ.

All supplementary tables and visualizations will be included in the final version of the paper or appendix.

We sincerely thank you for your valuable feedback and constructive suggestions. We are particularly encouraged by your recognition of LASQ as "elegant fusion", "novel strategy" and "tasteful philosophy". Below, we provide a point-by-point response to your comments.

Q1 & W1: Computational Cost

We have now added detailed computational complexity metrics below (NVIDIA A800, LOL dataset). We clarify that the coarse-to-fine MCMC sampling mechanism is only used during training and is embedded into the forward diffusion process. It guides the model to traverse luminance layers in a hierarchical manner, enabling structured learning of light propagation. During inference, our model only performs the denoising step conditioned on the low-light input within the diffusion model, which is significantly more efficient.

We compare LASQ against both early non-diffusion-based methods (e.g., EnlightenGAN, KinD++), and recent diffusion-based approaches (e.g., WCDM, LightenDiffusion). While the early methods are lightweight, their performance lags far behind diffusion-based models across all key metrics. Existing diffusion models, although significantly more effective, tend to suffer from high computational cost due to deep architectures and iterative sampling. LASQ, while maintaining the performance advantages of diffusion models, achieves inference efficiency comparable to non-diffusion-based methods. This makes it highly suitable for real-world deployment. Considering the substantial performance gain without reliance on reference images, the moderate computational overhead of LASQ is a practical and acceptable trade-off. In future work, we also plan to explore lightweight variants of our framework for further efficiency.

Q2: Robustness to Extreme Lighting

We would like to clarify that our approach employs a coarse-to-fine MCMC sampling strategy to fit the luminance adaptation space, rather than rigidly enforcing the power-law assumption. As discussed in Appendix A (paragraph 4), we reinterpret the strict power-law model as a relaxed prior and leverage MCMC sampling—integrated with the forward process of a diffusion model—to explore the distribution space.

This design enables LASQ to flexibly capture a wider family of luminance mappings that are only loosely guided by the physics-inspired prior, rather than being constrained to a fixed analytical form. As a result, our method does not critically depend on the power-law assumption itself. The MCMC-based inference operates at a structured level, incorporating spatial context, which allows it to remain robust under spatially inconsistent or extreme lighting conditions—well beyond the capabilities of per-pixel or strictly model-driven approaches.

To validate the robustness and stability of LASQ across diverse lighting conditions, we evaluate it on two additional datasets: DICM, featuring scenes with “intense background light”, and Light-Effects, containing “strong spotlights”. In the tables below, each metric is presented as DICM / Light-Effects. As shown, LASQ consistently achieves the best performance across all metrics on both datasets, demonstrating its strong effectiveness even under conditions that significantly deviate from the power-law assumption.

In addition to the datasets presented in the main paper and supplementary material (LOL, LSRW, NPE, VV, LIME, MEF), we also tested LASQ on several challenging unseen domains—LOL_blur, LED, and ELD. Due to space constraints, detailed results are provided in the responses to other reviewers. These experiments further demonstrate the strong generalization ability and robustness of LASQ across diverse and atypical low-light scenarios.

Q3 & W2: Hyperparameter Sensitivity

To address concerns about empirical parameter selection, we provide a hyperparameter sensitivity analysis on the LSRW dataset.

As illustrated in the table, we systematically varied key hyperparameters including $\alpha$, $\eta$, $\lambda_d$, and $\lambda_g$ over a range of values ($\beta_{p}$ is determined by $\eta$). The results show that while performance slightly fluctuates with different settings, the overall impact on metrics remains moderate. For instance, varying $\alpha$ between 0.05 and 0.6 only causes a minor PSNR change (within 0.3 dB) and negligible shifts in perceptual scores. Similarly, other hyperparameters demonstrate a stable trend without sharp degradation. These experiments demonstrate that our method is not overly sensitive to hyperparameter selection, and maintains consistently strong performance across a broad range of settings—highlighting its robustness, practical stability, and generalization potential.

Q4: Color Fidelity Evaluation

To validate our claim of improved color reproduction, we performed a comprehensive quantitative evaluation on the LOL dataset using three widely recognized metrics that assess perceptual color accuracy: CIE76 (ΔE*ab), CIEDE2000 (ΔE₀₀), and FSIMc. ΔE*ab and ΔE₀₀ measure perceptual differences in hue, luminance, and chrom, while FSIMc captures perceptual image quality by incorporating color similarity.

As shown, our proposed LASQ achieves the lowest color difference scores and the highest FSIMc, confirming its superior color fidelity. These results quantitatively support our claim that LASQ delivers more faithful and perceptually accurate color restoration compared to other methods.

All supplementary tables and visualizations will be included in the final version of the paper or appendix.