BlurDM: A Blur Diffusion Model for Image Deblurring

We thank the reviewer for recognizing the novelty of our approach and its significant performance gains shown in experiments. We greatly appreciate these encouraging comments. We address each concern in detail below and will revise the paper accordingly.

Weakness 1: About the standing among prior works and the performance of BlurDM to Uformer

Regarding the concern about the standing among prior works, we would like to clarify that our proposed method, BlurDM, is a plug-and-play framework with strong generalization ability, designed to integrate into arbitrary image deblurring backbones. To demonstrate this, we conducted comparisons in Table 1 against four widely recognized deblurring methods, including FFTformer, which was the state-of-the-art at the time of paper submission. These comparisons clearly validate that our framework can effectively enhance strong baseline architectures.

Additionally, as you suggested, we conduct experiments using Uformer as the deblurring backbone. As shown in Table G, our method consistently improves Uformer’s performance on the GoPro and HIDE datasets, verifying the effectiveness and robustness of our proposed approach across different architectures.

Table G: Performance comparison between Uformer and Uformer + BlurDM on GoPro and HIDE datasets.

Weakness 2: Performance comparison of the number of steps used in RDDM and our method

To ensure a fair evaluation in Table 3, we set the diffusion steps to five for all models. For additional insights, Table H presents a comparison of RDDM and BlurDM under varying numbers of diffusion steps, where PSNR and LPIPS are used to assess performance. RDDM achieves its peak PSNR of 32.08 dB at step 4 and the best LPIPS score of 0.0121 at step 10. In comparison, BlurDM achieves a higher peak PSNR of 32.28 dB at step 5 and a lower LPIPS score of 0.0113 at step 10. These results demonstrate that BlurDM consistently outperforms RDDM in terms of both distortion-based (PSNR) and perceptual (LPIPS) quality metrics.

Table H: PSNR↑ / LPIPS↓ under different step counts on the GoPro dataset. BlurDM shows superior performance in both fidelity and perceptual quality.

Question 1: The role of noise in blurred images

We would like to clarify that the “noise” in our dual diffusion framework does not refer to sensor noise in captured images. Instead, motivated by recent studies (Lines 108–123) highlighting the strong generative capabilities of diffusion models in reconstructing missing high-frequency details, we leverage the noise diffusion process to stochastically synthesize these lost high-frequency details in heavily blurred regions. This is conceptually different from modeling physical sensor noise. The discussion above will be incorporated into the paper.

Question 2: The performance of MiMo-UNet baseline reported in Tables 2 and 3

To ensure a fair comparison, we adopt different training schedules for different experimental purposes. Specifically, in Table 1, MIMO-UNet + BlurDM is trained with 3000 epochs for Stage 1, 500 for Stage 2, and 3000 for Stage 3. In contrast, Tables 2 and 3 use a standardized schedule of 1000/500/1000 epochs for the three stages to ensure consistency across methods in the ablation and component analysis. We will clarify it in the paper.

Dear reviewer,

Thank you for the comments on our paper.

We have submitted the responses to your comments. Please let us know if you have additional questions so that we can address them during the discussion period.

Thank you!

Best,

Authors

We appreciate your review. We hope our responses have addressed your concerns. As the discussion deadline is approaching, please let us know if you have further questions after reading our rebuttal. We aim to address all potential issues during the discussion period and hope that you will consider raising the score.

Thank you!

Best,

Authors

Dear Reviewer,

With only one day remaining in the discussion phase, we welcome any additional feedback you may have so that we can address all remaining concerns.

Authors

Hi Reviewer BwW8,

This is a gentle reminder to participate in the discussion with the authors regarding their rebuttal. Your input at this stage is important and appreciated.

Best, AC

We thank the reviewer for recognizing the robustness of our theoretical derivations, the modularity and flexibility of BlurDM, and the consistent performance gains demonstrated across extensive experiments. We greatly appreciate these encouraging comments. We address each concern in detail below and will revise the paper accordingly

Weakness 1: Generalizability of the BlurDM for defocus blur

We appreciate the comment regarding the generalizability. While we agree that this paper primarily focuses on motion deblurring, we wish to emphasize that motion blur stands as a persistently challenging and unresolved research topic in the literature of image restoration. It is evidenced that recent impactful works such as MIMO-UNet, Stripformer, FFTformer, and LoFormer focus exclusively on motion deblurring, highlighting the importance of addressing motion blur in this field. Additionally, although BlurDM is specifically designed to address motion blur, it can be flexibly integrated into general-purpose deblurring backbones capable of handling both motion and defocus blur. This allows BlurDM to provide motion-aware guidance that effectively enhances motion deblurring performance.

As a future direction, we plan to extend BlurDM by incorporating the physical characteristics of defocus blur into the diffusion process, similar to what we did in Equation (1) for motion blur. It enables a unified prior that addresses more complex and mixed blur types.

Weakness 2 and Question 1: Direct comparison with current diffusion-based deblurring models

As mentioned in Lines 62–64, prior studies have shown that applying diffusion models directly in the image space for deblurring often struggles to recover fine details due to the inherent stochasticity of the generative process. Moreover, image-space diffusion is computationally expensive and memory-intensive, particularly for high-resolution datasets like GoPro and RealBlur. Therefore, we focus on latent-space diffusion and conduct a fair comparison by evaluating different diffusion algorithms, including DDPM and RDDM, within the latent space using the same deblurring backbone, as shown in Table 3.

Additionally, we directly compare BlurDM with two recent diffusion-based deblurring methods, including HI-Diff [4] and RDDM [17], on the GoPro dataset, as shown in Table E. HI-Diff applies DDPM to the deblurring network in the latent space, whereas RDDM performs the residual diffusion process in the image space. BlurDM consistently achieves better performances in PSNR and SSIM under comparable parameter counts and FLOPs. Moreover, as a plug-and-play module, BlurDM can be flexibly integrated into various backbone architectures. This demonstrates not only its superior performance but also its strong generalizability across different network designs.

Table E: Comparison of different deblurring methods in terms of PSNR, SSIM, number of parameters, and FLOPs.

Weakness 3 and Question 2: Training cost of the three-stage training strategy

In Table F, we report the training complexity introduced by BlurDM in terms of training time and convergence behavior, using MIMO-UNet as the backbone. The default number of training epochs for MIMO-UNet is 3, 000, denoted as “Baseline 1”. Increasing the training epochs to 6, 000, denoted as “Baseline 2”, results in only a marginal improvement of 0.07 dB in PSNR. For BlurDM, we experiment with different training configurations, including using 1, 500 or 3, 000 epochs for Stage 1 and Stage 3, with 500 epochs for Stage 2. Both “BlurDM 1” and “BlurDM 2” outperform Baseline 2 while requiring less training time, demonstrating the effectiveness of the proposed three-stage training strategy. Finally, we adopt “BlurDM 3” as our final model, which increases training time by only 8% while achieving a 0.42 dB improvement in PSNR compared to “Baseline 2”.

As for convergence behavior, according to our observation of the learning curves, the optimization process does not suffer from any convergence issue. Furthermore, we will release all our code upon the paper’s acceptance to ensure reproducibility.

Table F: Comparison of training cost and performance between baseline and BlurDM.

Dear reviewer,

Thank you for the comments on our paper.

We have submitted the responses to your comments. Please let us know if you have additional questions so that we can address them during the discussion period.

Thank you!

Best,

Authors

We thank the reviewer for recognizing our idea as theoretically well-motivated and novel, and for acknowledging the promising experimental results. We greatly appreciate these encouraging comments and address the concern in detail below.

Questions 1: Supervision of blur residual $e_t$ during training

As detailed in Lines 512–525, we do not explicitly supervise the individual blur residuals $e_t$ during training. Instead, BlurDM is optimized using gradients derived from the reconstruction loss between the deblurred result $I^{\theta}_0$ and the ground-truth sharp image $I^0$ through Equation (36). Since BlurDM is a physics-guided module that estimates blur residuals based on the principles of blur formation, as formulated in Equation (12), it can effectively estimate these residuals without requiring ground-truth supervision for intermediate blur residuals. Despite the absence of intermediate ground-truth supervision, the deblurred results at different time steps shown in Figure 5 demonstrate that BlurDM effectively captures blur residuals throughout the reverse process.

Dear reviewer,

Thank you for the comments on our paper.

We have submitted the responses to your comments. Please let us know if you have additional questions so that we can address them during the discussion period.

Thank you!

Best,

Authors

We thank the reviewer for recognizing the strength of our core idea and the clear effectiveness of the proposed dual diffusion strategy in experiments. We greatly appreciate these encouraging comments. We address each concern in detail below and will revise the paper accordingly.

Weaknesses 1: Theoretical justification of latent-space BlurDM

Previous works, such as Stable Diffusion [a], HI-Diff [15], and Swin-diff [16], have demonstrated the effectiveness and efficiency of shifting the diffusion process from the image space to the latent space by leveraging latent space encoders such as VAEs and CNNs. Inspired by these methods, we employ sharp and blur encoders to learn latent representations for performing the diffusion process in the latent space through a three-stage training strategy. Specifically, in the forward diffusion process, instead of adding blur step by step to images, we derive a one-step blur addition process, as described in Appendix A.1. This process demonstrates that the final blurred and noisy image can be obtained by directly adding noise to the blurred image provided in the original dataset. In the reverse generation process, we utilize Equation (12) to iteratively remove blur features, following the principles of the blur formation process in the forward diffusion stage. Moreover, to demonstrate that our latent-space diffusion process performs deblurring in an iterative manner, we present deblurred results at different time steps in Figure 5, confirming that blur residuals are effectively addressed in the latent domain.

Reference:

[a] Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, Björn Ommer. High-Resolution Image Synthesis with Latent Diffusion Models. In CVPR, 2022.

Weaknesses 2: Question about the convergency of motion blur to the Gaussian distribution

As described in Equation (6), we model motion blur as a mean shift of the standard Gaussian diffusion process, where the mean is shifted by $\frac{1}{\alpha_T} \sum_{t=1}^{T}e_t$ that captures the degradation characteristics introduced by motion blur. This mean-shift interpretation is conceptually aligned with the idea presented in Figure 1 of the RDDM paper [17]. However, as mentioned in Lines 118–123, RDDM models the blur residual by "linearly'' computing the difference between the blurred and sharp image via subtraction. In contrast, we drive a dual denoising and deblurring formulation that follows the principles of the blur formation process to align with the natural characteristics of blur, typically caused by a "convolutional'' process.

Question 1 and Question 3: Effectiveness of the three-stage training strategy

In Table D, we present ablation studies to evaluate the effectiveness of the three-stage training strategy. We use MIMO-UNet as the backbone, and all models are trained for 1000 epochs to ensure a fair comparison. “Net1” denotes the baseline deblurring performance without incorporating BlurDM. In “Net2”, we directly use the sharp prior $Z^S$ in BlurDM, serving as an upper bound for the achievable deblurring performance. In “Net3”, we jointly optimize BlurDM and the deblurring model without pre-training through Stage 1 and Stage 2, serving as a baseline for a purely data-driven approach. In “Net4” and “Net5”, after completing pre-training in Stage 1, we apply either Stage 2 or Stage 3 alone to optimize BlurDM and the deblurring model. In “Net6”, we adopt the complete three-stage training strategy, which achieves the best performance compared to the alternative combinations used in “Net3” to “Net5”.

Table D: Ablation study of each training stage in BlurDM.

Question 2: Evaluation of BlurDM on real-world blur scenarios under varying conditions

In Table 1 of our main paper, we evaluate BlurDM on the challenging real-world dataset RealBlur, which contains naturally captured blur under low-light conditions, often accompanied by severe blur intensity and sensor noise. BlurDM consistently improves the performance of existing methods on the RealBlur dataset, achieving gains of up to 1.24 dB on RealBlur-J and 1.16 dB on RealBlur-R in PSNR, thereby verifying the robustness of our approach under diverse degradation conditions.

Dear reviewer,

Thank you for the comments on our paper.

We have submitted the responses to your comments. Please let us know if you have additional questions so that we can address them during the discussion period.

Thank you!

Best,

Authors

Thank you for the insightful review and positive feedback.

To further address your concern about weakness 1, we provide the theoretical derivation of latent BlurDM. Let $z_t = E(I_t)$, where $I_t$ is the blurred image at time step $t$, $E(\cdot)$ is the encoder, and $z_t$ is the corresponding latent feature. Using the first-order Taylor expansion of the encoder around $I_{t-1}$, we have:

$z_t \approx z_{t-1} + J_E(I_{t-1})(I_t - I_{t-1}),$

where $J_E(I_{t-1})$is the Jacobian of the encoder evaluated at$I_{t-1}$. From Equation (3) in the paper, it can be derived

$I_t - I_{t-1} = \left( \frac{\alpha_{t-1}}{\alpha_t} - 1 \right) I_{t-1} + \frac{1}{\alpha_t} e_t + \beta_t \epsilon_t.$

Plugging the above equation into the Taylor expansion yields:

$z_t \approx\ z_{t-1}+ J_E(I_{t-1}) \left( \frac{\alpha_{t-1}}{\alpha_t} - 1 \right) I_{t-1} + \frac{1}{\alpha_t} J_E(I_{t-1}) e_t + \beta_t J_E(I_{t-1}) \epsilon_t.$

Since $\frac{\alpha_{t-1}}{\alpha_t} \approx 1$ when the exposure intervals are sufficiently small, the expression simplifies to:

$z_t \approx \left( \frac{\alpha_{t-1}}{\alpha_t} \right) z_{t-1} + \frac{1}{\alpha_t} e_t^\theta + \beta_t \epsilon_t^\theta,$

where $\theta$ denotes the learnable parameters as shown in Equation (12). $e_t^\theta = J_E(I_{t-1}) e_t$ and $\epsilon_t^\theta = J_E(I_{t-1}) \epsilon_t$ represent the blur residual term and the noise term projected into the latent space, respectively. This demonstrates that the noise and blur terms in the latent BlurDM can be characterized and learned in the same way as the two corresponding terms in Equation (3).

Dear Reviewer,

With only one day remaining in the discussion phase, we welcome any additional feedback you may have so that we can address all remaining concerns.

Authors

We sincerely thank the reviewer for recognizing BlurDM’s novelty, technical rigor, and practical integration. We greatly appreciate these encouraging comments. We address each concern in detail below and will revise the paper accordingly.

Weaknesses 1 and Question 1: Fundamental Differences between DDPM, RDDM, and our BlurDM

As explained in Lines 35–45 and 108–117 of the paper, motion blur results from a continuous exposure process during image capture, where blur intensity accumulates progressively along a motion trajectory. This leads to highly structured and directionally consistent patterns, which differ significantly from the random noise perturbations modeled by conventional diffusion-based frameworks like DDPM.

Previous works [3, 4, 15, 30] that directly apply DDPM to image deblurring neglect this critical physical aspect of blur formation, thereby limiting their capacity to model the real-world blur formation process and ultimately resulting in suboptimal deblurring performance.

As mentioned in Lines 118–123, RDDM [17] models the blur residual by "linearly'' computing the difference between the blurred and sharp image via subtraction, which is inconsistent with real-world blur formation, typically caused by a "convolutional'' process.

In contrast, we drive a dual denoising and deblurring formulation in Equation (4) that adheres to the principles of the blur formation process, aligning with the natural characteristics of blur. In Table 3, BlurDM outperforms DDPM by $0.37$ dB on GoPro and $0.28$ dB on RealBlur-J, and outperforms RDDM by $0.25$ dB on GoPro and $0.23$ dB on RealBlur-J, clearly demonstrating the effectiveness of our blur-aware design.

Weaknesses 1: Significant Performance Gains and Field Impact

Table A presents the performance of annually SoTA image deblurring methods over the past three years, including Stripformer, FFTformer, and LoFormer. Taking the representative and real-world dataset RealBlur-R as an example, annual improvements on this dataset typically remain within 0.3 dB in PSNR. As shown in Table 1 of the paper, our proposed BlurDM significantly improves Stripformer, FFTformer, and LoFormer by 1.16 dB, 0.44 db, and 0.56 dB, respectively, on this dataset, which represents a significant and consistent advancement in image deblurring. Furthermore, the other four reviewers recognize BlurDM’s performance improvement as a key strength.

Table A: PSNR comparison on GoPro, HIDE, RealBlur-J, and RealBlur-R datasets using various backbones.

Weaknesses 2 and Question 3: Generalizability of the BlurDM for defocus blur

We appreciate the comment regarding the generalizability. While we agree that this paper primarily focuses on motion deblurring, we wish to emphasize that motion blur stands as a persistently challenging and unresolved research topic in the literature of image restoration. It is evidenced that recent impactful works such as MIMO-UNet, Stripformer, FFTformer, and LoFormer focus exclusively on motion deblurring, highlighting the importance of addressing motion blur in this field. Additionally, although BlurDM is specifically designed to address motion blur, it can be flexibly integrated into general-purpose deblurring backbones capable of handling both motion and defocus blur. This allows BlurDM to provide motion-aware guidance that effectively enhances motion deblurring performance.

As a future direction, we plan to extend BlurDM by incorporating the physical characteristics of defocus blur into the diffusion process, similar to what we did in Equation (1) for motion blur. It enables a unified prior that addresses more complex and mixed blur types.

Weaknesses 3 and Limitation 2: Analysis of real-world edge deployment

Our primary focus is to develop a novel and effective deblurring algorithm, like prior works, such as MIMO-UNet, Stripformer, FFTformer, and LoFormer. Our method achieves SoTA per- formance (reported in Table 1 of the paper) with reasonable computational costs in model size, FLOPs, and runtime (Table 4 of the paper). Despite its importance and practical implications, real-world deployment on edge devices is beyond the scope of this work.

Question 2: Memory usage and inference time of BlurDM on 4K images

BlurDM works in the latent space with the diffusion prior injected into the deblurring backbone in a channel-wise manner. This allows its efficient application to an arbitrary resolution input. In Table B, we evaluate the memory usage and inference time of BlurDM on 4K images using an NVIDIA RTX 3090 GPU, with MIMO-UNet as the backbone. BlurDM introduces minor overheads, increasing memory usage by only 7.4% and runtime by just 2.3%.

Table B: Memory usage and inference time on 4K images using an NVIDIA RTX 3090 GPU.

Question 4: Bootstrapped confidence intervals

Following recent deblurring methods such as MIMO-UNet, Stripformer, FFTformer, and LoFormer, we report average PSNR and SSIM scores for evaluation in the paper. As suggested, we conducted a bootstrapped confidence interval analysis using 1000-sample resampling from the test sets. Table C reports the 95% confidence intervals for PSNR values over four benchmark datasets (GoPro, HIDE, RealBlur-J, and RealBlur-R) using four different backbones (MIMO-UNet, Stripformer, FFTformer, and LoFormer). For each combination, we present the [min, max] bounds computed from the bootstrapped distribution of PSNR scores. BlurDM consistently yields better performance compared to the baseline, validating the robustness and significance of the improvements.

Table C: 95% confidence intervals of PSNR values across different backbones and datasets.

Limitation 1: Ethical risks

While deblurring techniques could potentially be misused on sensitive content (e.g., surveillance footage), our method is designed for beneficial applications such as autonomous driving, medical imaging enhancement, and video communication. We support responsible use and plan to explore safeguards to prevent potential misuse.

Dear reviewer,

Thank you for the comments on our paper.

We have submitted the responses to your comments. Please let us know if you have additional questions so that we can address them during the discussion period.

Thank you!

Best,

Authors

We appreciate your review. We hope our responses have addressed your concerns. As the discussion deadline is approaching, please let us know if you have further questions after reading our rebuttal. We aim to address all potential issues during the discussion period and hope that you will consider raising the score.

Thank you!

Best,

Authors

Dear Reviewer,

With only one day remaining in the discussion phase, we welcome any additional feedback you may have so that we can address all remaining concerns.

Authors

Thank you for your feedback. We address each concern in detail below.

Q1.1: Mathematical proof that subtraction inherently violates motion blur physics

In RDDM, the residual $I_{\text{res}}$ is explicitly defined as the blurred image minus the sharp image:

$I_{\text{res}} = I_{\text{in}} - I_0,$

where $I_\text{in}$ denotes the blur image and $I_0$ denotes the sharp image (see Section 4 in the RDDM paper). During the forward process, this fixed residual is linearly added to the sharp image $I_0$ over multiple steps:

$I_t = I_{t-1} + \alpha_t I_{\text{res}} + \beta_t \epsilon_{t-1},$

which progressively transforms $I_0$ into the blurred image $I_{\text{in}}$.

However, the real blur formation process is governed by the following continuous exposure integration:

$B = \frac{1}{\alpha_T} \int_0^{\alpha_T} H(\tau) \, d\tau,$

where each pixel’s intensity is the accumulated radiance along its motion trajectory, as mentioned in Lines 137-147 of our paper. This accumulation produces intermediate states that are themselves partial-exposure averages, not the result of linearly interpolating between a sharp image and a fully blurred image via a fixed residual.

Thus, RDDM’s design---subtracting sharp from blur to obtain a constant residual and adding it linearly---does not reflect the physics of motion blur formation, where intermediate images are generated by progressive integration over time, not by residual addition. In contrast, our BlurDM designs the diffusion process directly based on this physical model of motion blur, ensuring consistency with the actual exposure-based formation mechanism.

Q1.2: Table 3’s performance gaps (0.2--0.3dB) could stem from architectural differences rather than the proposed diffusion mechanism

In the experiments reported in Table 3, we ensured a fair comparison between RDDM and BlurDM by using the exact SAME model architecture, training pipeline, and hyperparameters. The only difference lies in the diffusion mechanism (subtractive residual in RDDM vs. our blur residual in BlurDM). Under this controlled setting, BlurDM consistently outperforms RDDM by 0.2–0.3 dB, which can therefore be attributed directly to the proposed diffusion mechanism rather than architectural factors.

Q2.1: Table C’s bootstrapped confidence intervals overlap between baselines and BlurDM-enhanced models (e.g., FFTformer on RealBlur-R: [39.72, 40.46] vs. [40.20, 40.90]). Gains are statistically marginal and visually insignificant

We would like to clarify that the range of a bootstrapped confidence interval is influenced by the variance of individual image scores within the test set. For FFTformer on RealBlur-R, BlurDM outperforms the baseline by +0.48 dB at the lower bound and +0.44 dB at the upper bound of the 95% confidence interval. Moreover, Table 1 shows that BlurDM achieves an ``average gain'' of +0.44 dB across the entire test set. In the image deblurring literature, typical annual improvements are around +0.3 dB (as shown in Table A), indicating that our gain is significant.

Regarding visual quality, we follow the standard evaluation protocol adopted by widely recognized deblurring methods, such as MIMO-UNet, Stripformer, FFTformer, and LoFormer, and report the performance in PSNR and SSIM, along with qualitative comparisons. As shown in Figures 3 and 4, BlurDM produces visually sharper and more faithful reconstructions compared to its baselines, further supporting the effectiveness of our approach.

Q2.2: Table B’s ``minor overhead'' (7.4% memory, 2.3% runtime for 4K images) ignores deployment constraints—adding 1.5GB VRAM and 58ms latency is prohibitive for edge devices

We would like to emphasize that we make no claim of pursuing lightweight deblurring or edge-device-specific optimization. Our method is designed and evaluated under the same GPU-based experimental settings used in widely recognized deblurring studies, including MIMO-UNet, Stripformer, FFTformer, and LoFormer. These works, like ours, focus on developing new algorithms and model architectures for high-quality image deblurring rather than on lightweight designs for edge devices. Therefore, our computational overhead should be interpreted in the context of fair, GPU-targeted benchmarking against these baselines.

It is worth noting that in our setting, a 7.4% VRAM increase and 2.3% runtime increase for 4K images is relatively minor compared to the gains in PSNR and SSIM reported in Tables 1–-3. For many practical applications running on workstations or server GPUs, this trade-off is acceptable and aligns with the resource profiles of existing SOTA methods.

Q2.1: visually insignificant (no perceptual metrics like LPIPS or user studies provided).

Table I demonstrates that BlurDM consistently outperforms the baseline across four datasets and four backbones, indicating its effectiveness in enhancing visual quality.

Table I: Quantitative comparison of baseline models and BlurDM on four benchmark datasets (GoPro, HIDE, RealBlur-J, RealBlur-R) using LPIPS.

Hi Reviewer zo6Q,

This is a gentle reminder to participate in the discussion with the authors regarding their rebuttal. Your input at this stage is important and appreciated.

Best, AC