{"id":"152a9e42-3dda-4c06-bbf7-3978eede33f0","arxiv_id":"2511.18471","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"AdaPS adaptively scales likelihood guidance in DDIM posterior sampling via agreement between two surrogates, improving LPIPS/PSNR trade-offs on image restoration tasks without task-specific tuning.","lead":"AdaPS automatically sets how strongly a diffusion model obeys noisy measurements during image reconstruction, removing per-task tuning. It reports better perceptual quality with similar fidelity on super-resolution and deblurring benchmarks.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. 24's noise-space mapping is algebraically inconsistent with Eq. 7, so the d_t magnitude used in the adaptive coefficient is not the derived one; the 'hyperparameter-free' step size therefore rests on an unexamined rescaling.","rationale":"The reader's weakest_assumption concerned the factor-of-two bias correction and its universality. That is a real concern, but the more load-bearing issue is upstream: the magnitude of d_t itself appears to be derived incorrectly in Eq. 24. Since xi*_t is the ratio of inner products involving d_t, a wrong d_t directly changes the adaptive step size, and the fixed factor 2 cannot compensate for a time-dependent 1/(1 - alpha_bar_t) discrepancy. This makes the method's 'principled' and 'hyperparameter-free' framing questionable, even if the empirical results are reproducible. The proposed check—re-deriving the algebra and re-running one central experiment with the corrected d_t—would settle whether this is a typographical error or a substantive flaw. The reader already gave a conditional verdict due to code absence, missing error bars, and Eq. 24's factor inconsistency; my concern strengthens that condition but does not move the overall verdict, so UNCHANGED is appropriate.","tokens_in":15910,"tokens_out":10124,"duration_ms":97230,"concrete_test":"Independently re-derive d_t from Eq. 23 and Eq. 7 without using Eq. 24. Then re-run the ImageNet-256 SR x4 sigma_y = 0.05 experiment with the corrected d_t (sqrt(alpha_bar_t)/sqrt(1 - alpha_bar_t) coefficient), keeping Eq. 19's factor 2 unchanged. If PSNR/LPIPS shift more than ~0.1 dB / 0.01 LPIPS, the published update does not implement the claimed derivation and the 'hyperparameter-free' claim is materially weakened. If results match the paper, the discrepancy is a typo and the method is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central adaptive rule in Eq. 19 depends on d_t, which Eq. 24 defines as d_t = sqrt(alpha_bar_t) * sqrt(1 - alpha_bar_t) * A^T (AA^T + sigma_y^2 / r_t^2 I)^-1 (A x_hat_0 - y). But combining Eq. 23 with the VP noise mapping Eq. 7 gives d_t = eps*_t - eps_theta,t = (x_t - sqrt(alpha_bar_t) x*_0)/sqrt(1 - alpha_bar_t) - (x_t - sqrt(alpha_bar_t) x_hat_0)/sqrt(1 - alpha_bar_t) = -sqrt(alpha_bar_t)/sqrt(1 - alpha_bar_t) (x*_0 - x_hat_0). Using Eq. 23, this yields sqrt(alpha_bar_t)/sqrt(1 - alpha_bar_t) A^T (AA^T + sigma_y^2 / r_t^2 I)^-1 (A x_hat_0 - y), not sqrt(alpha_bar_t) * sqrt(1 - alpha_bar_t). Thus Eq. 24 is off by a time-dependent factor 1/(1 - alpha_bar_t), which diverges as t -> 0. Since xi*_t is the projection of d_t onto g_t, this factor directly changes the update magnitude. It cannot be absorbed into the fixed factor 2. Consequently, the paper's 'principled' derivation does not, as written, yield the update in Eq. 19; the effective scaling is partly heuristic. The empirical gains may still be real, but the central claim of a derived, hyperparameter-free rule is not supported without correcting this inconsistency and verifying the implementation.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The submission is internally inconsistent: the title and abstract describe a \"Jacobian-Aware Posterior Sampling (JAPS)\" method, while the full text presents \"Adaptive Posterior diffusion Sampling (AdaPS)\". Taking the full text as the actual contribution, the paper proposes AdaPS, which incorporates a likelihood-score surrogate g_t into the DDIM update (Eq. 15) and selects the guidance coefficient ξ_t by least-squares projection of a posterior-noise residual d_t onto g_t (Eq. 16). d_t is approximated via a MAP estimate of x_0 given (x_t, y) under a Gaussian approximation (Eqs. 23–24), and the update includes an empirical factor-of-two bias correction (Eq. 19). The method is evaluated on super-resolution, Gaussian deblurring, and motion deblurring on CelebA-HQ and ImageNet-256, plus a nonlinear deblurring extension. The experimental sections are extensive, but the derivation contains a concrete algebraic error and an empirically fitted constant that undermine the theoretical claims.","tokens_in":16411,"tokens_out":11399,"duration_ms":105395,"significance":"If the derivation were sound, the contribution would be significant: an adaptive, multi-task guidance scaling that preserves DDIM scheduling, avoids Jacobian computation in the magnitude, and attains a favorable perception–distortion trade-off. The experimental breadth is a strength: two datasets, three tasks, noisy/noiseless settings, ablations over step count, noise, stochasticity, and surrogate pairings, and a cross-validated ΠGDM reimplementation. The reported LPIPS gains (e.g., Table 1, ImageNet motion deblurring: 0.147 for AdaPS-ΠGDM vs 0.205 for DDPG) are meaningful. However, Eq. (24) is algebraically wrong and the factor-of-two correction is an empirical fit; as written, the central claim of a \"principled, hyperparameter-free\" sampler is not established. The significance is therefore conditional on fixing the derivation and validating the fitted constant.","major_comments":[{"comment":"The manuscript's title and abstract describe 'Jacobian-Aware Posterior Sampling (JAPS)' with a 'corrected conditional factor', but the body introduces 'Adaptive Posterior diffusion Sampling (AdaPS)' and never defines JAPS. For example, the abstract claims the method 'bridges direct and proximal approaches' and 'leverages the Jacobian's prior knowledge', while §3's derivation uses d_t from an \\hat{x}_0-space MAP residual and g_t chosen as DPS or ΠGDM. This is not cosmetic: the reader cannot verify which method is being presented. Harmonize the title, abstract, and body before review can be completed.","section":"Abstract / Title; §1–§3"},{"comment":"Combining Eq. (7), Eq. (9), and Eq. (23) gives ε*_t − ε_θ,t = [(x_t − √ᾱ_t x*_0) − (x_t − √ᾱ_t \\hat{x}_0)]/√(1−ᾱ_t) = (√ᾱ_t/√(1−ᾱ_t))(\\hat{x}_0 − x*_0). Substituting Eq. (23) yields d_t = (√ᾱ_t/√(1−ᾱ_t)) A^T(AA^T + σ_y²/r_t² I)^{-1}(A\\hat{x}_0−y), not the √ᾱ_t√(1−ᾱ_t) in Eq. (24). The error is by a factor 1/(1−ᾱ_t), which diverges as t→0. Because d_t enters ξ*_t, ⟨d_t,g_t⟩, and the update Eq. (19), the implemented update is not the derived one; the missing factor cannot be absorbed into the fixed factor 2. This is a load-bearing inconsistency. The same expression appears in Eq. (34). Please correct the derivation and state whether the implementation uses the corrected factor or the printed one.","section":"§3.2.2, Eq. (24); also Eq. (34)"},{"comment":"The 'simple, data-agnostic bias correction, scaling by 2≈1/E[⟨d̂_t, ĝ_t⟩] (empirically≈0.5 at mid-trajectory)' is an empirical fit, not a derived constant. No supporting measurement of the alignment statistic is shown, and it may vary with task, noise level, step count, and diffusion time. This contradicts the 'hyperparameter-free' claim and makes the update magnitude partly heuristic. Furthermore, correcting Eq. (24) will change d_t and hence the statistic, so the factor 2 may no longer be valid. Provide evidence of its stability or revise the claims.","section":"§3.2.1, Eq. (19)"},{"comment":"The nonlinear extension replaces J(x_0)^T J(x_0) with λ(x_0) I_n (Eq. 30) and fixes λ_damp>0 and K=5 (after Eq. 33). Fixed constants are still hyperparameters; fixing them across tasks does not make the method 'essentially hyperparameter-free.' Since only one nonlinear task (Table 3) is shown, the robustness of these constants is not established. This is secondary, but should be addressed if the nonlinear claim is retained.","section":"B.1, Eqs. (30)–(33)"}],"minor_comments":[{"comment":"In §3.2.1, g_t is used in Eq. (16) without the normalization mentioned in Supplement C ('when using any likelihood surrogate for g_t, it is normalized'). Define g_t consistently in the main text.","section":"§3.2.1 / Supplement C"},{"comment":"The caption says 'Values in gray are excluded because they were obtained with a larger number of sampling steps,' but no gray values are distinguishable in the rendered text. Mark excluded entries explicitly.","section":"Table 1, caption"},{"comment":"The equivalence between Eq. (24)'s d_t and \\tilde{ε}^{MAP}_θ in Eq. (34) is not stated. Align the notation so the surrogate definitions are easy to compare.","section":"Eq. (24) / Eq. (34)"},{"comment":"The Limitations say the derivation 'leverages the linear–Gaussian setting for clarity and efficiency,' but Eq. (23) depends on the linear-Gaussian form. The statement that extension to nonlinear/non-Gaussian models is possible 'in principle' should be qualified by the approximate nature and the extra constants introduced in B.1.","section":"§5, Limitations"}],"recommendation":"major_revision","confidential_remarks":"The submitted file appears to combine two different manuscript versions (JAPS abstract/title with AdaPS body). This is an editorial red flag: please ask the authors to clarify the intended version. Also, code is withheld until acceptance, and the key alignment statistic underlying the factor 2 is not documented, which limits reproducibility."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper on arXiv 2511.18471 is mislabeled: the metadata title/abstract describe a 'Jacobian-Aware Posterior Sampler' (JAPS), but the body is AdaPS, an adaptive guidance-scale method for diffusion posterior sampling. If you read it, read the body.\n\nWhat's actually new: the conditional DDIM reformulation with gamma_t is a useful correction (many methods add likelihood gradients without that coefficient); the alignment-based adaptive step size (projection of a MAP residual d_t onto the likelihood direction g_t) is a neat idea; and the MAP surrogate to avoid the denoiser Jacobian is practical. On the empirical side, the paper shows consistent LPIPS gains with modest PSNR cost vs DDPG, PGDM, DiffPIR, etc., on SR and deblurring on two datasets, and the ablations on step count, noise, stochasticity, and surrogate pairings are genuinely informative.\n\nSoft spots: the main derivation has a factor error. Eq. 24 claims d_t = sqrt(alpha_bar_t)*sqrt(1-alpha_bar_t) A^T(...)^{-1}(A xhat0 - y). But combining Eq. 23 with the VP relation xt = sqrt(alpha_bar_t) x0 + sqrt(1-alpha_bar_t) epsilon gives d_t = sqrt(alpha_bar_t)/sqrt(1-alpha_bar_t) A^T(...)^{-1}(A xhat0 - y). The paper is off by a time-dependent factor 1/(1-alpha_bar_t), which diverges as t -> 0. So the d_t used in the adaptive coefficient is not the derived posterior-noise residual. The factor-2 bias correction is then an empirical fit, not part of a principled derivation. That undercuts the 'hyperparameter-free' claim. There are also no error bars, no code, and the title/abstract mismatch suggests the paper wasn't polished at submission.\n\nTo be fair: the empirical wins may still hold; the adaptive rule could work even with the wrong constant, and the ablations show it beats fixed scales. But the derivation as written doesn't justify the update.\n\nThis paper is for researchers working on zero-shot diffusion inverse problems. It deserves a serious referee, but it needs a major revision: fix Eq. 24, release code, add error bars, align the title/abstract with the content, and soften the hyperparameter-free claim.\n\nRecommendation: send to peer review, with expectation of substantial revision.","headline":"Empirically promising adaptive guidance sampler, but Eq. 24 has a time-dependent factor error that undercuts the 'derived' step size; send to review with expectation of major revision.","tokens_in":16837,"tokens_out":5282,"would_cite":false,"duration_ms":50412,"reading_group":"yes","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A hyperparameter-free alignment rule sets the likelihood step in diffusion posterior sampling, claiming better perceptual quality with little or no distortion loss, across inverse problems.","keywords":["diffusion models","inverse problems","posterior sampling","adaptive guidance","DDIM","image restoration","hyperparameter-free","likelihood approximation"],"falsifier":"Measure the per-timestep average of the cosine similarity between the two likelihood surrogates on a task the paper does not test, such as inpainting or phase retrieval at 256px; if it departs from 0.5 by more than roughly 0.1 over the mid-trajectory, the factor-2 rule is miscalibrated. Directly comparing AdaPS with a fixed factor 2 against a version using a per-task fitted factor would settle whether the universal constant is correct.","tokens_in":15805,"feed_emoji":"🖼️","tokens_out":5049,"duration_ms":50984,"temperature":0.7,"pith_summary":"AdaPS is a way to set the strength of the data-fidelity (likelihood) update in diffusion-based posterior sampling, a step that previous methods tune per task or fix by schedule. The paper shows that the right step size is the projection coefficient between two complementary surrogates of the intractable likelihood gradient: when the surrogates agree, take a larger step; when they conflict, shrink it. It also identifies a missing scaling factor in the DDIM reformulation that earlier likelihood insertions ignored, so the guidance scales correctly with step count and stochasticity. Across super-resolution and deblurring tasks, the paper reports that AdaPS matches or beats prior samplers on perceptual quality (LPIPS) with minimal or no PSNR loss, without task-specific tuning.","feed_headline":"One alignment score replaces tuned guidance in diffusion restoration","feed_subtitle":"AdaPS sets the likelihood step by surrogate agreement, raising perceptual quality without losing distortion.","key_machinery":"The load-bearing object is the projection coefficient ⟨d_t, g_t⟩/||g_t||² between two approximations of the intractable likelihood score. d_t is a MAP-based residual computed in the denoised-image space without the denoiser Jacobian, while g_t is a likelihood direction that may include the Jacobian. The DDIM coefficient γ_t multiplies the whole correction, and the factor 2 is a data-agnostic bias correction for the systematic shrinkage caused by imperfect alignment. Splitting magnitude (Jacobian-free) from direction (potentially Jacobian-aware) is what lets the method avoid ill-conditioned step sizes while preserving useful Jacobian information.","core_discovery":"Under the linear-Gaussian measurement model and a Gaussian approximation of the intermediate clean-signal posterior, the paper derives a closed-form MAP residual in noise space that approximates the difference between the optimal posterior noise and the unconditional denoiser's noise prediction, without backpropagating through the denoiser. The final update is x_{t-1} = DDIM(x_t) - 2γ_t (⟨d_t, g_t⟩/||g_t||²) g_t, where g_t is any likelihood-direction surrogate, d_t is the Jacobian-free MAP residual, γ_t is the DDIM coefficient, and the factor 2 compensates for the empirically observed ~0.5 cosine alignment between the two surrogates. The paper argues this yields a principled, hyperparameter-","pith_inferences":["The alignment statistic could be monitored online during sampling; replacing the fixed factor 2 with a moving average of the cosine similarity would make the method adaptive to tasks where the 0.5 assumption fails.","The agreement heuristic doubles as a confidence diagnostic: when the two likelihood surrogates strongly disagree, the update is automatically attenuated, which may explain the method's robustness to high measurement noise.","If a latent-diffusion version could define both surrogates in latent space, the schedule-robustness demonstrated here would plausibly carry over, provided the alignment statistic remains informative in that space."],"forward_implications":["Posterior samplers built on unconditional diffusion priors no longer need per-task step-size tuning; the alignment rule sets the scale automatically.","The missing scaling factor means earlier likelihood insertions were miscalibrated; including it makes guidance scale with step count and stochasticity, so more diffusion steps continue to improve perceptual quality.","Splitting magnitude from direction gives a stable compromise that avoids overweighting ill-conditioned directions while keeping the benefit of Jacobian information, without extra computational cost.","The same construction extends to nonlinear measurement operators through a scalar Gauss-Newton MAP refinement with fixed hyperparameters.","Because the method is hyperparameter-free, it transfers across tasks and noise levels without re-fitting, which prior approaches generally require."],"fun_headline_variants":["Diffusion inverse problems solved with Jacobian-aware sampling","New sampler bridges direct and proximal diffusion approaches","Jacobian-aware posterior sampler boosts image restoration","Zero-cost Jacobian guidance improves diffusion inverse problems","Bridging diffusion methods with a Jacobian-aware posterior sampler"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The fixed factor-of-two bias correction assumes that throughout the trajectory the expected cosine similarity between the two likelihood surrogates is close to 0.5 in every task, dataset, and noise level; if the true mean alignment differs, the guidance magnitude is systematically wrong.","fun_headline_variants_meta":{"raw":{"variants":["Diffusion inverse problems solved with Jacobian-aware sampling","New sampler bridges direct and proximal diffusion approaches","Jacobian-aware posterior sampler boosts image restoration","Zero-cost Jacobian guidance improves diffusion inverse problems","Bridging diffusion methods with a Jacobian-aware posterior sampler"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000187,"raw_usage":{"total_tokens":1159,"prompt_tokens":730,"completion_tokens":429,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":474,"completion_tokens_details":{"reasoning_tokens":356}},"tokens_in":474,"tokens_out":429,"duration_ms":4335,"temperature":1.0,"reasoning_tokens":356,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T20:43:25.547134+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the per-timestep average of the cosine similarity between the two likelihood surrogates on a task the paper does not test, such as inpainting or phase retrieval at 256px; if it departs from 0.5 by more than roughly 0.1 over the mid-trajectory, the factor-2 rule is miscalibrated. Directly comparing AdaPS with a fixed factor 2 against a version using a per-task fitted factor would settle whether the universal constant is correct.","supporting_citations":[],"review_version":1}