Title: DGSolver: Diffusion Generalist Solver with Universal Posterior Sampling for Image Restoration
Venue: NeurIPS 2025
Accepted: yes
Keywords: Image restoration

diffusion generalist solver

universal posterior sampling

deep learning
Abstract: Diffusion models have achieved remarkable progress in universal image restoration. However, existing methods perform naive inference in the reverse process, which leads to cumulative errors under limited sampling steps and large step intervals. Moreover, they struggle to balance the commonality of degradation representations with restoration quality, often depending on complex compensation mechanisms that enhance fidelity at the expense of efficiency. To address these challenges, we introduce \textbf{DGSolver}, a diffusion generalist solver with universal posterior sampling. We first derive the exact ordinary differential equations for generalist diffusion models to unify degradation representations and design tailored high-order solvers with a queue-based accelerated sampling strategy to improve both accuracy and efficiency. We then integrate universal posterior sampling to better approximate manifold-constrained gradients, yielding a more accurate noise estimation and correcting errors in inverse inference. Extensive experiments demonstrate that DGSolver outperforms state-of-the-art methods in restoration accuracy, stability, and scalability, both qualitatively and quantitatively. Code and models are publicly available at https://github.com/MiliLab/DGSolver.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a training-free solver for diffusion generalist models, termed as DGSolver. First, it reformulates the diffusion process as ODEs and exploits the semi-linear integral structure to better approximate the solutions. This avoids the computational overhead of training a series of networks for quality refinement. Second, it integrates the estimated residual term I_{res} into diffusion posterior sampling to construct the universal sampling mechanism, which guides the sampling process universally without the prior knowledge of degradation formulation. These two components enhance the restoration accuracy and efficiency across a variety of degradation tasks. Overall, the proposed method demonstrates notable theoretical novelty, practical applicability, and broad adaptability.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n\n1.This paper presents a rigorously derived and technically sound ODE integrator with accelerated sampling strategy for accurate sampling from diffusion models to achieve quality refinement, which can be widely exploited and benefited by other related methods.\n\n2.The proposed UPS is novel and clever, and does not require the prior knowledge or estimation of degradation formulation. It can cope with various types of degradation without complicated designs with high potential.\n\n3.All the framework is well motivated and the explanations are clear. The authors effectively provide a theoretical derivation and error analysis of the proposed method.\n\n4.Comprehensive experiments are carried out on multiple datasets, various tasks, and different domains, fully demonstrating the proposed method’s superior performance over state-of-the-art methods both quantitatively and qualitatively.\n\n**Weaknesses**\n\n1.The expressions for $\\alpha(t)$, $\\beta(t)$, and $\\gamma(t)$ in Eq.(4) lack clarity.\n\n2.Some of the notations in the appendix lack definitions and some typos need to be corrected (e.g., $I_\\text{res}^{\\theta}$ is misspelled in Appendix F). It would be worthwhile to spend some effort to make that better.\n\nQUESTIONS:\n1.How do you choose the sampling steps or variable $t$ in the reverse process? What are the relationships between time step $t$ and predefined parameters $\\alpha(t)$, $\\beta(t)$, and $\\gamma(t)$ in Eq.(4)? I think it is important for readers to understand the paper and implementation.\n\n2.Please provide the computational complexity analysis before and after applying the queue-based sampling strategy.\n\n3.When dealing with compound degradation, the model can restore degraded images in a specific order, which seems to be determined spontaneously by the unified model. Could the authors share some insights on achieving controllable restoration in the given order or handling all degradation types in one execution for compound degraded images based on the proposed method?\n\nLIMITATIONS:\nYes, the authors have discussed the related limitations.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-21"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents DGSolver, a novel framework designed to balance the commonality of degradation representations with restoration quality in diffusion models. DGSolver mitigates accumulated discretization errors through tailored high-order solvers with a universal posterior sampling strategy, and further enhances sampling efficiency by introducing a queue-based accelerated sampling strategy.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. The paper provides a thorough and rigorous derivation of the proposed method, demonstrating a solid theoretical foundation.\n\n2. The proposed high-order solvers and universal posterior sampling strategy are intuitively illustrated in the figure, effectively clarifying their fundamental principle.\n\n3. Experimental results demonstrate the effectiveness of the proposed method from qualitative, quantitative perspectives.\n\nWeaknesses:\n\n1.The ablation study should quantitatively compare model parameters, sampling steps, and inference time with baseline DiffUIR[1] to better demonstrate the superiority of the proposed method.\n\n2.Lack of quantitative comparison with the latest state-of-the-art methods proposed in 2025. \n\n3.Table 4 shows that increasing the number of sampling steps beyond a certain point leads to a decline in PSNR/SSIM. Could the authors provide insight into this counterintuitive result?\n\n4.Why were the experimental settings (datasets and training parameters) from the baseline DiffUIR not adopted?\n\n5.The motivation for designing the forward process as a stochastic differential equation (SDE) is unclear. Its practical significance remains questionable, as no explicit analysis or justification is provided in the experiments.\n\n6.The expression “total M+1 time steps” in line 146 is inconsistent with the notation presented in Figure 2.\n\n7.In Figure 5, the position of blue boxes is inconsistent.\n\n8.In Tables 2, 3, and 4, the best results should be highlighted in bold.\n\nQUESTIONS:\n1.The Universal Posterior Sampling (UPS) strategy demonstrates clear performance benefits in this work. Could UPS also be applied to other existing methods?\n\n2.Is the queue-based sampling strategy affecting model performance while improving efficiency?\n\n3.Does increasing the order of the high-order solvers influence the efficiency of inference?\n\nLIMITATIONS:\nThe limitations have been discussed in the supplementary materials.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes DGSolver, a training-free diffusion-based solver for image restoration that unifies a custom reverse-time ODE, high-order solvers, and universal posterior correction. It introduces a semi-linear forward process using a residual-based degradation model and derives tailored solvers to efficiently recover clean images.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n1. The use of high-order solvers tailored to the semi-linear structure of the reverse process introduces a novel and principled way to reduce the number of sampling steps in diffusion-based restoration.\n2. The solver design is clearly presented, with a queue-based implementation that enables efficient computation of higher-order derivatives without redundant evaluations.\n3. Evaluation is very thorough and shows improvement over comparison methods.\n4. Ablation studies are well-designed and support the impact of key components such as solver order and universal posterior correction (UPC).\n\n**Weaknesses:**\n1. The main ideas are valuable but somewhat difficult to follow due to dense presentation and unconventional notation. A more streamlined explanation with clearer separation of key components would improve accessibility.\n2. The forward process relies on the definition $I_{res}=I_{in}-I_0$, which implies additive degradations in aligned domains. While appropriate for denoising-like tasks, this formulation does not generalize to inverse problems such as super-resolution, MRI, or operator-unknown deblurring, where the degradation is either non-additive or defined in a different domain. Given that $I_{res}$ plays a central role in both the forward and reverse processes, this assumption limits the applicability of DGSolver to a narrow set of problems, despite its claim to universality.\n\nMinor comments:\n- The blue zoomed-in insets in Figure 5 appear inconsistent as the regions shown for the rainy input and ground truth differ from those in the restored results.\n- Line 94, “…computationally intractability...” -> computationally intractable\n- Line 111, “when” -> When\n\nQUESTIONS:\n1.\tSection 3.3 appears heavily influenced by Diffusion Posterior Sampling (DPS), yet the original paper is not cited or discussed in this section. Can the authors clarify what is novel in their Universal Posterior Sampling (UPS) approach beyond the omission of an explicit measurement operator? Additionally, why is the original DPS work not acknowledged in the relevant discussion?\n2.\tThe results in Table 4 feel a bit unintuitive to me. It’s not clear why using exactly 8 steps leads to better performance than 9 or 10. I would normally expect performance to improve as the number of sampling steps increases. Is there a natural explanation for this behavior?\n3.\tCan the authors comment on sample variety?\n\nLIMITATIONS:\nYes, the authors have addressed the limitations in the Appendix F.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces DGSolver, a novel diffusion generalist solver with universal posterior sampling for image restoration. It addresses the limitations of existing diffusion models in universal image restoration, which suffer from cumulative errors in reverse inference and the trade-off between degradation representation commonality and restoration quality. The authors derive exact ODEs solution for diffusion generalist models and develop high-order solvers with a queue-based accelerated sampling strategy to enhance accuracy and efficiency. Additionally, they integrate universal posterior sampling to improve noise estimation and correct errors in inverse inference. Extensive experiments demonstrate that DGSolver outperforms state-of-the-art methods in restoration accuracy, stability, and scalability across various tasks and datasets.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths:\n1. The reformulation of the generalist diffusion process using ODEs and the development of customized high-order solvers with a queue-based accelerated sampling strategy are novel contributions to the field of image restoration.\n2. The integration of universal posterior sampling provides a versatile and effective way to enhance the accuracy of noise estimation and correct errors, leading to improved restoration quality.\n3. The proposed method is validated through experiments on multiple image restoration tasks, such as deraining, low-light enhancement, etc., and shows superior performance over existing methods.\n\n### Weaknesses:\n1. The reformulation of the generalist diffusion process using ODEs and the development of customized high-order solvers have been extensively explored in image generation, and their application to image restoration is a natural extension.\n2. The paper proposes a queue-based accelerated sampling strategy. However, its effectiveness might be limited in few-step sampling scenarios, and the paper lacks ablation studies to verify its performance in such cases.\n3. While $\\bar{\\delta}_T$ controls degradation commonality, the paper does not systematically explore its effect on specific degradation types.\n4. Although zero-shot results on real-world datasets are presented, the evaluation lacks quantitative metrics for unpaired real data, relying solely on visual comparisons\n\nQUESTIONS:\n1. What challenges or opportunities arise from applying the generalist diffusion process reformulated with ODEs and customized high-order solvers, which are common in image generation, to the field of image restoration?\n2. Given that k=2 with UPS already achieves near-optimal performance, what is the practical benefit of higher-order solvers (k=3) in terms of restoration quality versus computational cost? Can you provide a trade-off analysis (e.g., FLOPs vs. PSNR) for different k?\n3. The paper mentions the use of a queue-based accelerated sampling strategy. Could this method remain effective when using fewer sampling steps? Typically, high-order solvers are designed to accelerate sampling with fewer steps.\n4. The optimal $\\bar{\\delta}_T=1$ is used for complex degradations, but does this generalize to all tasks? For example, does deraining benefit from a different $\\bar{\\delta}_T$ than deblurring?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nOverall, this work is a strong paper with both theoretical depth and clear empirical improvements over previous universal methods.\nThe authors reformulate the restoration process as a semi-linear ODE that can be solved analytically, and they derive a closed form integral solution for the ODE. This derivation uses an inverse transformation for the nonlinear parts, assuming those parts are monotonic and invertible functions. They expand these nonlinear integrals with Taylor series and retain terms up to a chosen order k, and obtain a family of k-th order update formulas. Authors show that earlier diffusion restoration methods can be considered as the first order case of their solver.\nOverall, the proofs around proposition 1 are solid and novel in the context of diffusion restoration.\n\nNext, authors provide a theoretical upper bound for the approximation error (Jensen's gap where the outer expectation over the posterior is replaced by inner expectations with respect to the data distribution). They show the error depends on the variance of the measurement noise and the accuracy of the model’s predictions, guaranteeing that the error is controlled (for linear inverse problems with Gaussian noise) in Theorem 1.\n\nAuthors' claims are well supported by the empirical results, showing strong SoTA performance among universal methods and on par performance compared to task specific methods.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n1. The paper proposes the novel idea to combine exact ODE solution + universal posterior sampling, generalizing prior diffusion restoration methods. \n2. Theoretical derivations are clear.\n3. Empirically, they show strong SOTA results across tasks and datasets. \n\n\nWeaknesses:\n1. Authors don't provide FPS/runtime throughput data on full-resolution images. Also, they don't provide data on actual inference time or memory usage.\n\nQUESTIONS:\n1. Equation (4) has a typo; $q_{0t}$ should be $q_{0}$?\n\n2. Equation (21), is this $l_{2}$ norm $∥⋅∥^2 $?\n\n3. Could you show a direct ablation against another method like DiffUIR using their own solver vs. DGSolver to isolate the solvers contribution?\n\nLIMITATIONS:\nTheorem 1 provides a rigorous bound for the posterior approximation error only for linear measurement models, although many degradations ops are inherently nonlinear and hence not covered.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}