{"id":"f18dbb4e-bc4b-459e-aace-c8346f756bda","arxiv_id":"2505.22923","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A plug-and-play Gibbs sampler that uses two diffusion priors, one for the image and one for the blur kernel, outperforms prior blind-deblurring methods on synthetic kernel benchmarks.","lead":"Blind-PnPDM is a new algorithm that solves blind image deblurring, where both the image and the blur kernel are unknown, by alternating between two diffusion-model priors inside a sampling loop. It reports better PSNR, SSIM, and LPIPS than existing deblurring pipelines on 100 FFHQ test images with synthetic Gaussian and motion kernels.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Split-Gibbs target mismatch undermines the posterior-sampling claim; Eqs. (6)-(9) describe an approximate surrogate, not p(x,theta|y).","rationale":"The reader's weakest_assumption was about the EDM prior step and convergence to the joint posterior. I agree that convergence is unexamined, but the more precise and load-bearing problem is that the algorithm's SGS decomposition is not targeting Eq. (5) even in the idealized case. Equation (6) states x^(k+1) is drawn from the conditional posterior exp(-f(x;theta,y) - g(x)); Eq. (8) draws from exp(-g(x) - ||x-z||^2/(2 rho_x^2)) after a z that lives in a Gaussian-smoothed likelihood. The composition has a different stationary distribution. The theta-update has the same issue, and the printed likelihood step for theta is dimensionally inconsistent. This does not require reading diffusion-model approximations as the culprit; the bias is structural and would persist with oracle conditionals. The concrete Gaussian test would settle the question immediately. Because the empirical results may still hold and the flaw is correctable by rephrasing the contribution as approximate posterior sampling and adding a bias analysis, I would keep the reader's CONDITIONAL verdict rather than escalate to rejection. The paper needs to correct the equations and add this diagnostic before the posterior-sampling claim is acceptable.","tokens_in":7570,"tokens_out":14109,"duration_ms":147648,"concrete_test":"On a small tractable problem (e.g., x in R^2, scalar kernel theta, Gaussian priors, y=A(theta)x+e), replace the diffusion prior steps with their exact Gaussian conditionals, so the only deviation from Eq. (5) is the split-Gibbs structure. Run Algorithm 1 with the paper's rho schedules, compute the empirical stationary distribution of (x,theta), and compare it with the true posterior p(x,theta|y) by KL divergence or Wasserstein distance. This isolates whether the algorithm targets Eq. (5) at all; if the distributions differ, the paper must reframe its central claim or provide a quantitative bias analysis.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that Algorithm 1 samples from the joint posterior p(x,theta|y) of Eq. (5). It does not, as written. The x-block is a split-Gibbs sampler: LikelihoodStepx draws z from exp(-f(z;theta,y) - ||x-z||^2/(2 rho_x^2)) and PriorStepx draws x from exp(-g(x) - ||x-z||^2/(2 rho_x^2)) (Eq. 8). The stationary distribution of this two-step block is therefore the augmented target pi(x,z|theta) proportional to exp(-f(z;theta,y) - g(x) - ||x-z||^2/(2 rho_x^2)); integrating out z gives a marginal for x proportional to exp(-g(x)) times the Gaussian-smoothed likelihood integral exp(-f(z;theta,y)) N(x;z,rho_x^2 I) dz, which is not exp(-f(x;theta,y) - g(x)) stated in Eq. (6). The theta-block in Eq. (9) has the same structure. Hence, even with a perfect EDM implementation of the prior steps, the chain converges to an approximate, rho-smoothed posterior, not to Eq. (5). No bias bound or diagnostic is given, and the annealing schedules in Section 3 stop at rho_x=0.1 and rho_theta=0.05, so the approximation is not removed. A separate textual problem: the printed LikelihoodStep_theta samples v in R^b from exp(-1/2 ||y - A(theta^(k)) v||^2 - ...), which is dimensionally invalid for kernel parameters and ignores x^(k+1); if the intended expression is A(v)x^(k+1), the smoothing bias above remains. The empirical comparison may be valid as a heuristic, but the 'posterior sampling' claim does not follow from the equations provided.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes Blind-PnPDM, an alternating plug-and-play posterior sampling method for blind inverse problems in which both the image and the measurement operator are unknown. Two diffusion models are used as priors, one for the image and one for the forward-model parameters, within a Split Gibbs Sampler (SGS) framework. Each conditional update is further decomposed into a likelihood step and a prior step, with the prior steps implemented as EDM reverse passes. The method is validated on blind image deblurring with Gaussian and motion kernels, reporting quantitative gains over Pan-DCP, DeblurGANv2, BlindDPS, and GibbsDDRM in PSNR, SSIM, and LPIPS. The central claim is that Algorithm 1 samples from the joint posterior p(x, theta | y) of Eq. (5).","tokens_in":7998,"tokens_out":5733,"duration_ms":53847,"significance":"Blind inverse problems are an important and under-served area for PnP sampling methods, and the idea of using two diffusion priors in an alternating denoising scheme is timely and potentially useful. The reported quantitative improvements over strong diffusion-based baselines (GibbsDDRM, BlindDPS) are encouraging, and the paper addresses a real gap in the PnP literature. However, the manuscript's central theoretical claim—that Algorithm 1 samples from the joint posterior—is not supported by the equations as written, and the empirical evaluation lacks error bars, multiple runs, and code. These issues are load-bearing for the paper's main claims, although the method may well be salvageable as an approximate/heuristic sampling scheme with additional analysis and diagnostics.","major_comments":[{"comment":"The paper claims that Algorithm 1 samples from the joint posterior p(x, theta | y) of Eq. (5), but this does not follow from the equations. The x-block is a split-Gibbs block with augmented target pi(x,z | theta) proportional to exp(-f(z; theta, y) - g(x) - ||x - z||^2/(2 rho_x^2)); integrating out z gives a stationary marginal for x proportional to exp(-g(x)) times the Gaussian-smoothed likelihood integral exp(-f(z; theta, y)) N(x; z, rho_x^2 I) dz, which is not the exp(-f(x; theta, y) - g(x)) stated in Eq. (6). The theta-block in Eq. (9) has the same structure. The annealing schedules in Section 3 stop at rho_x = 0.1 and rho_theta = 0.05, so the smoothing bias is not removed, and no bias bound or diagnostic is provided. The empirical results may remain valid as a heuristic, but the posterior-sampling claim does not follow from the presented equations.","section":"Section 2.2, Eqs. (6)-(9), Algorithm 1"},{"comment":"The displayed update for v^(k) is dimensionally inconsistent: v is in R^b, but the quadratic term uses A(theta^(k)) v. In the blind deblurring model A(theta) x = theta * x, so A(theta^(k)) v is not defined when v is a kernel parameter. If the intended expression is A(v) x^(k+1), then the printed equation ignores the current image x^(k+1) and contradicts the conditional target in Eq. (7). This must be corrected because it directly affects the reproducibility of Algorithm 1 and the meaning of the theta-block.","section":"Section 2.2, LikelihoodStep_theta"},{"comment":"The implementation of Eq. (8) and Eq. (9) by a single EDM reverse pass from t* with sigma(t*) = rho is inherited from PnPDM, but no argument is given in this paper that such a pass samples the conditional density exp(-g(x) - ||x - z||^2/(2 rho_x^2)) or the analogous kernel density in the blind setting. The original PnPDM justification is not automatically transferred here because both priors are now conditioned on auxiliary variables from different modalities, and the paper provides no empirical diagnostic (e.g., conditional sample quality or chain mixing) to support the approximation. This is load-bearing: if the prior steps are not accurate, the chain is not even targeting the augmented distributions described by Eqs. (8)-(9).","section":"Section 2.1, PriorStepx and PriorStep_theta"},{"comment":"The quantitative comparison is based on a single run with no error bars, no multiple seeds, and no ablation of the coupling schedules rho_x and rho_theta. For a sampling method, single-sample metrics are particularly sensitive to randomness in the diffusion reverse passes; without such information, the reported margins (e.g., PSNR 27.42 vs 25.94 for motion blur) cannot be distinguished from sampling noise. Please report mean and standard deviation over multiple seeds and include an ablation of the annealing schedule, or at least a sensitivity analysis for rho_x and rho_theta.","section":"Section 3, Table 1"}],"minor_comments":[{"comment":"Equations (6) and (7) use '=' to equate a distribution with an unnormalized density; the right-hand sides are proportional to the conditional posteriors. Please use 'proportional to' notation consistently throughout.","section":"Section 2.1, Eqs. (6) and (7)"},{"comment":"The text refers to the baseline 'DeblurGAN' while Table 1 lists 'DeblurGANv2'; please align the names in the text, table, and reference list.","section":"Section 3"},{"comment":"Figures 1 and 2 are referenced but not included in the manuscript; the captions mention squares at the top displaying estimated kernels, but the qualitative claims cannot be evaluated without the figures.","section":"Figures 1 and 2"},{"comment":"The claim that Blind-PnPDM is 'the first PnP sampling method for blind inverse problems' is strong given references [28] and [30], which relate to block-coordinate PnP for blind inverse problems and split-Gibbs sampling with deep priors; please soften or clarify the novelty claim.","section":"Section 4, Conclusion"},{"comment":"The kernel diffusion model is described only as trained for '5M steps with a small U-Net'; the architecture, optimizer, learning rate, and training schedule are not specified, which limits reproducibility.","section":"Section 3, kernel diffusion model training"}],"recommendation":"major_revision","confidential_remarks":"The main gap is between the title/abstract claim of posterior sampling and the actual equations: the SGS construction in Section 2.2 targets a rho-smoothed surrogate rather than p(x, theta | y), and the LikelihoodStep_theta equation appears to contain a dimensional error. These are fixable by reframing the paper as an approximate/heuristic PnP sampler with careful diagnostics, or by adding a rigorous limiting argument, so I recommend major revision rather than rejection. The experimental section also needs error bars and ablation studies before the empirical claim can be accepted."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a straightforward hybrid: it takes PnPDM's split-Gibbs posterior sampler and runs it in a blind setting, alternating between an image diffusion prior and a kernel diffusion prior. Experiments on FFHQ blind deblurring show it beats BlindDPS and GibbsDDRM on PSNR, SSIM, and LPIPS. That is a real, if modest, empirical result. The method is easy to understand and reproduce from the description, which is a virtue.\n\nThe problem is the claim that it samples from the joint posterior of Eq. (5). The split-Gibbs steps in Section 2 do not converge to that target. The x-block's stationary distribution is exp(-g(x)) times the Gaussian-smoothed likelihood, not exp(-f(x;theta,y)-g(x)). The theta block has the same structure. With annealing floors of rho_x=0.1 and rho_theta=0.05, the bias is not removed. The paper offers no bias bound or diagnostic. I also noticed the LikelihoodStep_theta formula samples v in R^b using A(theta^(k))v, which is dimensionally inconsistent; presumably they meant A(v)x^(k+1). That typo suggests the derivation was not checked carefully. The absence of code, error bars, and ablations on the schedules further weakens the paper as a standalone contribution.\n\nNone of this is a red flag for fraud. The method probably works as a heuristic, and the empirical comparison is honest. But the theoretical language oversells what is actually a plausible alternating approximation. If they reframe the paper as an empirical method for blind deblurring, correct the typo, and add at least one repeat with standard errors and a sensitivity check on rho, it would be a solid conference paper.\n\nWho benefits: researchers in computational imaging who want a concrete recipe for using diffusion priors over both image and kernel. I would send it to peer review rather than desk reject, but with the expectation that the authors fix the theoretical overclaim and the missing reproducibility details. A serious referee can help make it useful.","headline":"Clean empirical extension to blind PnP sampling, but the posterior-sampling claim doesn't survive a close read of the split-Gibbs target.","tokens_in":8518,"tokens_out":2958,"would_cite":true,"duration_ms":28911,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Blind-PnPDM claims that blind inverse problems—where both the target image and the measurement operator are unknown—can be solved by posterior sampling that alternates between two Gaussian denoising steps, each driven by a pre-trained…","keywords":["blind inverse problems","plug-and-play methods","diffusion models","posterior sampling","split Gibbs sampling","blind image deblurring","kernel estimation","Gaussian denoising"],"falsifier":"Run Blind-PnPDM many times on the same blurred input with different random seeds and initializations and examine the spread of the reconstructed images and kernels. If all runs collapse to nearly the same point instead of producing a distribution of plausible image/kernel pairs consistent with the observation, the alternating chain is not sampling the joint posterior and the posterior-sampling interpretation fails.","tokens_in":7367,"feed_emoji":"🖼️","tokens_out":9477,"duration_ms":88055,"temperature":0.7,"pith_summary":"Blind-PnPDM targets blind inverse problems, where the observation is produced by an unknown measurement operator acting on an unknown image, and recasts recovery as posterior sampling instead of point estimation. The method places two pre-trained diffusion models in a plug-and-play sampler, one acting as the image prior and one as the prior over the operator parameters, and alternates between sampling the image given the current operator and sampling the operator given the current image. Each conditional sampling step is split into a Gaussian likelihood update and a denoising prior update, so the joint estimation problem becomes a sequence of Gaussian denoising subproblems. On blind image deblurring with Gaussian and motion kernels, the paper reports that this scheme outperforms Pan-DCP, DeblurGANv2, BlindDPS, and GibbsDDRM in PSNR, SSIM, and LPIPS, while also producing kernel estimates that look closer to the ground truth.","feed_headline":"Two diffusion models recover image and blur kernel together","feed_subtitle":"Blind-PnPDM alternates denoising steps for image and kernel, beating diffusion baselines on PSNR, SSIM, and LPIPS.","key_machinery":"The load-bearing mechanism is an alternating split-Gibbs sampler with two pre-trained diffusion-model priors. In the image conditional, an auxiliary variable $z$ is sampled from a Gaussian distribution combining the data-fidelity term $\\|y-A(\\theta)z\\|_2^2/2$ with the coupling $\\|x^{(k)}-z\\|^2/(2\\rho_x^2)$, and then the prior step samples $x\\sim\\exp(-g(x)-\\|x-z\\|^2/(2\\rho_x^2))$ by running one reverse pass of an Elucidated Diffusion Model (EDM) from the noise level $\\sigma(t^*)=\\rho_x$ down to zero. The operator conditional uses the same construction with a second diffusion model $D_\\beta$ and its own auxiliary variable $v$ and coupling strength $\\rho_\\theta$. Annealing schedules that decrease $\\rho_x$ and $\\rho_\\theta$ over the $K$ iterations are included to accelerate mixing and reduce the chance of getting stuck, and the two diffusion priors are the only learned components.","core_discovery":"The central claim is that the joint posterior $p(x,\\theta\\mid y)$ for the unknown image $x$ and unknown operator parameters $\\theta$ can be sampled by alternating two conditional Gibbs steps, each split into a likelihood step and a diffusion prior step. Auxiliary variables $z$ and $v$ are coupled to $x$ and $\\theta$ through quadratic penalties, making the likelihood steps Gaussian sampling problems in the measurement model and the prior steps exactly the task of denoising $z$ and $v$. Blind-PnPDM implements each prior step as a single reverse pass of a pre-trained EDM diffusion model initialized at the noise level corresponding to the coupling strength, which is the PnPDM recipe transplanted to the blind setting. The experimental claim is that on blind deblurring this alternating denoising scheme beats existing blind-deblurring baselines—including diffusion-based blind solvers—on PSNR, SSIM, and LPIPS, with reconstructed kernels that are more consistent with the ground truth.","pith_inferences":["A test the paper does not run: compare Blind-PnPDM against an oracle that uses the true kernel distribution as the prior. Matching the oracle would confirm the gains come from the sampling scheme; a gap would point at the kernel diffusion prior's approximation error.","The same two-prior alternating construction could be pointed at deconvolution microscopy or blind inpainting by swapping only the likelihood step's measurement model, since the prior steps are agnostic to the forward operator.","If the joint posterior is really being sampled, the framework offers calibrated uncertainty over blur kernels, which would be useful for downstream tasks like motion estimation or optical aberration correction; this uncertainty interpretation is implicit but unquantified in the paper."],"forward_implications":["On blind image deblurring with Gaussian and motion kernels, Blind-PnPDM reports higher PSNR and SSIM and lower LPIPS than Pan-DCP, DeblurGANv2, BlindDPS, and GibbsDDRM.","The framework needs no per-problem calibration or retraining: the same two pre-trained diffusion priors are inserted through the denoising steps, and only the likelihood model changes with the forward operator.","Because the operator prior lives over the parameter vector $\\theta$, the same alternating sampler extends to other blind inverse problems with low-dimensional operator parameterizations, such as blind super-resolution or parallel MRI.","Treating recovery as sampling rather than optimization means repeated runs with different randomness can in principle produce a spread of plausible image/kernel pairs, giving a form of uncertainty information about the solution.","The kernel estimates produced by the method are visually closer to the ground-truth kernels than those of the diffusion-based baselines, not just the images."],"supporting_citations":[{"why":"Supplies the PnPDM formulation and the EDM-based prior-step implementation that Blind-PnPDM extends to the blind setting.","marker":"[31]"},{"why":"Supplies the split Gibbs sampler that decomposes each conditional distribution into likelihood and prior steps.","marker":"[35]"},{"why":"Defines the EDM noise and scaling schedules used to turn denoising strength into a diffusion reverse-pass initialization.","marker":"[36]"},{"why":"Provides the kernel diffusion model training recipe and test kernel generation, and serves as the BlindDPS baseline.","marker":"[39]"},{"why":"Provides the GibbsDDRM baseline, a partially collapsed Gibbs sampler for blind inverse problems.","marker":"[43]"},{"why":"Supplies the FFHQ test images used for quantitative evaluation.","marker":"[37]"},{"why":"Supplies the pre-trained image diffusion model used as the image prior.","marker":"[38]"},{"why":"Provides the DeblurGANv2 supervised baseline for comparison.","marker":"[42]"},{"why":"Provides the Pan-DCP optimization baseline for joint image and kernel estimation.","marker":"[41]"}],"fun_headline_variants":["Dual diffusion models jointly recover image and blur kernel","Alternating denoising with two diffusion priors solves blind deblurring","Blind-PnPDM: Bayesian sampling for unknown image and kernel","Two diffusion models flip-flop to deblur without knowing the blur","Joint posterior sampling of image and operator via diffusion denoising"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that one reverse pass of a pre-trained diffusion model faithfully samples the denoising posterior for both the image and the blur kernel, so the alternating chain converges to the joint posterior; this is assumed, not proved or diagnosed, in the blind setting.","fun_headline_variants_meta":{"raw":{"variants":["Dual diffusion models jointly recover image and blur kernel","Alternating denoising with two diffusion priors solves blind deblurring","Blind-PnPDM: Bayesian sampling for unknown image and kernel","Two diffusion models flip-flop to deblur without knowing the blur","Joint posterior sampling of image and operator via diffusion denoising"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.0002,"raw_usage":{"total_tokens":1355,"prompt_tokens":905,"completion_tokens":450,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":521,"completion_tokens_details":{"reasoning_tokens":358}},"tokens_in":521,"tokens_out":450,"duration_ms":5394,"temperature":1.0,"reasoning_tokens":358,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T12:56:39.516803+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run Blind-PnPDM many times on the same blurred input with different random seeds and initializations and examine the spread of the reconstructed images and kernels. If all runs collapse to nearly the same point instead of producing a distribution of plausible image/kernel pairs consistent with the observation, the alternating chain is not sampling the joint posterior and the posterior-sampling interpretation fails.","supporting_citations":[{"cited_title":"Principled probabilistic imaging using diffusion models as plug-and-play priors,","cited_arxiv_id":null,"evidence_quote":"Supplies the PnPDM formulation and the EDM-based prior-step implementation that Blind-PnPDM extends to the blind setting."},{"cited_title":"Split-and-augmented gibbs sampler—application to large-scale inference problems,","cited_arxiv_id":null,"evidence_quote":"Supplies the split Gibbs sampler that decomposes each conditional distribution into likelihood and prior steps."},{"cited_title":"Elucidating the design space of diffusion-based generative models,","cited_arxiv_id":null,"evidence_quote":"Defines the EDM noise and scaling schedules used to turn denoising strength into a diffusion reverse-pass initialization."},{"cited_title":"Parallel diffusion models of operator and image for blind inverse problems,","cited_arxiv_id":null,"evidence_quote":"Provides the kernel diffusion model training recipe and test kernel generation, and serves as the BlindDPS baseline."},{"cited_title":"Gibbsddrm: A partially collapsed gibbs sampler for solving blind inverse problems with denoising diffusion restoration,","cited_arxiv_id":null,"evidence_quote":"Provides the GibbsDDRM baseline, a partially collapsed Gibbs sampler for blind inverse problems."},{"cited_title":"A style-based generator architecture for generative adversarial networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the FFHQ test images used for quantitative evaluation."},{"cited_title":"Come-closer-diffuse-faster: Accelerating conditional diffusion models for inverse problems through stochastic contraction,","cited_arxiv_id":null,"evidence_quote":"Supplies the pre-trained image diffusion model used as the image prior."},{"cited_title":"Deblurgan-v2: Deblurring (orders-of-magnitude) faster and better,","cited_arxiv_id":null,"evidence_quote":"Provides the DeblurGANv2 supervised baseline for comparison."},{"cited_title":"Deblurring images via dark channel prior,","cited_arxiv_id":null,"evidence_quote":"Provides the Pan-DCP optimization baseline for joint image and kernel estimation."}],"review_version":1}