{"id":"74a2205f-9420-451a-b5e4-5063ad58db3b","arxiv_id":"2608.02937","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":8,"one_line_summary":"ScoreField couples contrast and current neural fields with a frozen score prior to regularize full-wave electromagnetic inverse scattering, reporting the best PSNR on simulated and Fresnel benchmarks.","lead":"ScoreField is a neural inverse-scattering method that combines two neural field networks with a pretrained diffusion-style score prior, optimizing both against the full-wave Lippmann-Schwinger equations. On simulated phantoms and experimental Fresnel measurements, it reports higher reconstruction fidelity than classical full-wave solvers and learned baselines, including a stated average gain of 1.8 dB in PSNR on the two real Fresnel targets.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper never ablates the score-prior term, so the reported gains could come from the coupled-INR full-wave optimizer alone; Fig. 5 shows pre-injection and final states but no no-score endpoint.","rationale":"The reader identified score-model fidelity as the weakest assumption, and that is a real concern. My read points to a more elementary gap: even if the score model were perfectly accurate, the paper does not demonstrate that the score term contributes to the final result. There is no controlled ablation within ScoreField that turns the prior gradient off while keeping everything else identical. The comparison against LS-DnCNN and Imaging Interiors changes multiple components simultaneously, so the empirical gains in Tables 1 and 2 cannot be uniquely attributed to the score prior. This matters because the title, abstract, and Section 3.3 all frame the score prior as the key innovation. The Fig. 5 trajectories show large improvement between iteration 3000 and later iterations, but those later iterations also continue to optimize the full-wave loss, so they do not isolate the score update. I therefore keep the reader's CONDITIONAL verdict: the method is plausible and well-engineered, but the central causal claim needs either a matched on/off ablation or explicit evidence that the score term changes the final reconstruction. I do not see grounds to reject, because the reported results are internally consistent and the missing ablation is a testable omission rather than a demonstrated failure.","tokens_in":27715,"tokens_out":6330,"duration_ms":64195,"concrete_test":"Run a matched ablation on the 24 FFHQ strong-scattering test images: fix all hyperparameters in Algorithm 1 but set alpha_k=0 for k>k_warm, so steps 9-10 are skipped, and optimize the same coupled INRs for the same 10,000 Adam iterations with the same warm-up and schedules. Compare final PSNR/SSIM/LPIPS to Table 1. If the no-score run reaches or exceeds 26.16 dB, the score prior is not load-bearing; if it is at least 1 dB lower, the attribution is supported. Repeat the same on/off comparison for the FoamDielExt Fresnel case, with alpha set to zero after iteration 10, to test whether the reported 1.8 dB average gain over the best competing method survives without the prior gradient.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that adding a frozen score-model gradient to the coupled-INR Lippmann–Schwinger optimizer is what improves reconstruction fidelity. Algorithm 1 always applies the score update after the warm-up phase, and no experiment runs the same optimizer with the score term disabled. Fig. 5 shows snapshots before score injection (e.g., k=3000, PSNR 18.29 on FFHQ strong) and the final reconstruction with score on, but continued full-wave optimization alone is never evaluated. The baselines do not serve as within-method controls: LS-DnCNN uses a different prior mechanism (a denoiser) within a different proximal scheme, and Imaging Interiors omits the score prior but also differs in network size, RFF encoding, and loss normalization. Thus the reported improvements over baselines could be attributable to the INR architecture, coordinate jitter, RFF bandwidth, or loss design rather than to the score prior itself. This is not an internal inconsistency, but it is the load-bearing step for the paper's causal attribution. It also compounds the reader's concern about score-model fidelity: if s_phi is biased, a properly weighted score term could even hurt, and without an on/off comparison we cannot tell whether the term is helping, neutral, or being outweighed by other components. The reconstruction trajectories are suggestive but not conclusive, because optimization beyond iteration 3000 would likely improve the full-wave loss alone.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes ScoreField, a test-time optimization framework for nonlinear electromagnetic inverse scattering. It represents the unknown permittivity contrast and the induced currents with two coupled implicit neural representations (INRs), enforces the Lippmann–Schwinger state and data equations through a full-wave loss, and adds the output of a frozen score-based generative model as a prior-gradient direction on the contrast INR. The method is evaluated on simulated FFHQ strong- and weak-scattering benchmarks, the Austria phantom, and two experimental Fresnel datasets, with comparisons against classical full-wave solvers, plug-and-play denoiser baselines, an INR-based solver, and a supervised U-Net baseline. The authors report consistent PSNR/SSIM/MS-SSIM/LPIPS improvements, including a 1.8 dB average PSNR gain over the best competing method on the Fresnel data, and include a prior-mismatch robustness study and a Monte Carlo dropout calibration analysis.","tokens_in":27920,"tokens_out":3896,"duration_ms":39840,"significance":"The intended contribution is timely and plausible: combining a learned generative prior with an explicit full-wave forward model addresses a real limitation of both handcrafted-regularizer solvers and end-to-end learned inversions. The physical formulation is clearly derived and the choice of induced-current parameterization is well justified, including a useful supplementary analysis showing equivalence to the scattered-field parameterization and the Born-zero-initialization property. The evaluation is broad, spanning weak and strong scattering, simulated and experimental data, and uses a reasonable set of baselines. The paper also ships unusually complete implementation details in the supplementary material, including hyperparameters and baseline tuning procedures, and it explicitly discloses the relation to the authors' earlier CISA 2025 precursor [30]. If the causal effect of the score prior were established, the method would be a solid contribution to computational imaging and inverse scattering.","major_comments":[{"comment":"The central claim that the score-based prior is responsible for the reported improvements is never tested. Algorithm 1 always starts with a physics-only warm-up and then applies the score update for every subsequent iteration; no experiment runs the same optimizer with α_k ≡ 0 (or with k_warm = K) for the full 10,000 or 1,500 iterations. The baselines cannot serve as controls because they differ in network architecture, RFF encoding, coordinate jitter, loss normalization, and optimization schedule. Figure 5 shows snapshots before score injection but not the full-wave-only endpoint at the final iteration. Please add an on/off ablation of the score term, ideally with several prior-weight schedules, and report the same metrics for the no-score endpoint. Without this, the attribution in the abstract and conclusion is unsupported.","section":"Sec. 3.3 / Algorithm 1 / Tables 1–2"},{"comment":"No error bars or statistical tests are reported anywhere in the paper. In the weak-scattering FFHQ table, ScoreField's PSNR margin over UNet-BP is 0.13 dB and over LS-DnCNN is 0.25 dB; on FoamDielInt, the SSIM and LPIPS margins over LS-TV are 0.002. With n=24 FFHQ images and no reported per-image standard deviation, these differences are indistinguishable from run-to-run variation. The abstract claims the method 'significantly improves' reconstruction fidelity, but the data as presented support only a statement about point estimates. Please report per-image error bars, confidence intervals, or paired significance tests; if these are unavailable, the significance claim should be weakened accordingly.","section":"Tables 1 and 2; FFHQ weak-scattering and Fresnel results"},{"comment":"The mismatch test is weaker than the text claims. The 'mismatched' polygon prior is generated from circles, ellipses, rectangles, triangles, and irregular polygons, so for the Austria ring-and-disk phantom and the Fresnel two-cylinder targets the prior already contains the relevant shape classes; only layout, intensity, and clutter differ. The conclusion that 'the measured data can correct structures favored by a mismatched prior' would be much stronger with a prior whose shape class is disjoint from the target (for example, a texture or natural-image prior for Austria). In addition, the paper never quantifies how well s_ϕ approximates the true score at the σ_k values used in Eq. (26), which is the load-bearing modeling assumption behind the prior update. A quantitative score-error check or a sensitivity study over σ_min and α_k would address this concern.","section":"Sec. 5.1, prior-mismatch robustness"}],"minor_comments":[{"comment":"The normalization of f_θ to [−1,1] is not fully specified; please state the exact mapping (presumably 2 f_θ / f_max − 1) and confirm that the score network's output is consistently rescaled to the same convention as its training data.","section":"Algorithm 1, step 9"},{"comment":"The manuscript defines G as a dense N×N matrix but does not describe how the domain Green's function is applied in practice for N=128×128; please state whether FFT-based convolution is used for ScoreField itself, as is done for the Imaging Interiors baseline in the supplementary material.","section":"Sec. 3.2 and supplementary material"},{"comment":"The discussion explaining why ScoreField's Austria SSIM is lower than that of LS-DnCNN and UNet-BP is reasonable, but it would be more convincing if the per-window SSIM maps or a scale-dependent metric were shown, rather than relying on a qualitative statement about small boundary shifts.","section":"Sec. 4.2, Austria SSIM discussion"},{"comment":"The Monte Carlo dropout calibration analysis is described as preliminary, which is appropriate, but the text should state how the per-pixel intervals are formed from the 100 dropout samples and how the reported ECE values are averaged across the 24 images; the current description is too terse to reproduce.","section":"Sec. 5.2, Figure 6"},{"comment":"There are numerous minor typesetting issues (e.g., missing spaces in 'ScoreField,' 'permittivitycontrast,' 'Pre-print'), and the figure captions in the supplementary material are duplicated or mislabeled; a careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The central mechanism—the score-prior gradient—is never ablated, and without that ablation the paper's main causal claim is not established. The missing error bars are also a serious issue for a journal submission, particularly for the small margins in the weak-scattering and FoamDielInt tables. I do not see this as a reject: the formulation is sound, the evaluation is broad, and the requested experiments (score on/off, error bars, stronger mismatch test) are within scope. I would encourage the editor to request a major revision with the ablation as the primary requirement."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth a read if you work on learned priors for nonlinear inverse problems. The method is a clean integration of a frozen score prior with two coupled INRs under the Lippmann–Schwinger equations, and the evaluation is broader than most INR work: weak and strong scattering simulations, the Austria phantom, and real Fresnel data. The core idea is not circular—the score model is pretrained on unpaired images, and each reconstruction is instance-specific. The reported Fresnel gains of 1.2–2.5 dB are credible if the runs are as described, and the supplementary material gives genuinely useful implementation detail, including the FFT-convolution adaptation for Imaging Interiors and a careful derivation of why the induced-current parameterization is cleaner than the scattered-field one.\n\nThe biggest soft spot is exactly what the stress-test flags: the score term is never ablated. Algorithm 1 always injects the prior after warm-up; no experiment runs the same optimizer with the score term disabled. Since the baselines differ in architecture, RFF encoding, and loss normalization, they are not within-method controls. So the improvement over Imaging Interiors and LS-DnCNN could come from the coupled-INR setup itself rather than from the score direction. That is the load-bearing step for the paper's novelty, and it is unsupported as presented. A reviewer should ask for a score-on/off comparison using the identical INR and loss, plus some quantification of score-model error or sensitivity to the noise schedule.\n\nSecond, there are no error bars anywhere. Some margins are small—0.13 to 0.25 dB in weak-scattering FFHQ—so the word \"significantly\" is not supported there, even if the larger Fresnel and Austria margins are more convincing. The prior-mismatch robustness test is also weaker than claimed: the polygon prior includes circles, and the Austria and Fresnel targets are circular or disk-based, so the mismatch is only partial. The reconstruction trajectories do show the full-wave data correcting prior-induced structures, which is a good sign, but the OOD claim needs a more disjoint prior.\n\nThe math looks sound: the data and state losses are correctly formed, the normalization choices are explained, and the supplementary's discussion of current versus scattered-field coordinates is useful. The self-reference to the CISA precursor is explicitly disclosed, and the citation pattern is appropriate.\n\nWho it is for: computational imaging researchers, especially those working on score-based priors or INR-based full-wave solvers. A serious referee should engage with this—the method is promising, the evaluation is solid, and the missing ablation is fixable. I would send it to review with a clear request for the score on/off comparison and uncertainty quantification, but not desk-reject it.","headline":"Worth a serious referee: a broad, credible INR+score integration for full-wave inverse scattering, but the missing score-term ablation leaves the paper's central causal claim unproven.","tokens_in":28558,"tokens_out":2085,"would_cite":true,"duration_ms":21656,"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":"ScoreField couples a frozen score-based prior with Lippmann-Schwinger physics inside two neural fields, cutting artifacts and raising PSNR by about 1.8 dB over the best competing method on real measured scattering data.","keywords":["inverse scattering","score-based generative prior","implicit neural representation","Lippmann-Schwinger equation","multiple scattering","full-wave reconstruction","computational imaging","measured microwave data"],"falsifier":"Reconstruct a ring-and-disk phantom with a score model trained only on images that contain no disks or rings, and compare against the physics-only LS-TV baseline: if the score-guided run is not better, the claimed prior benefit is not robust to mismatch. Alternatively, estimate the true score at the chosen $\\sigma_{\\mathrm{min}}$ on held-out normalized contrasts and compare with $s_\\phi$; a large discrepancy there would mean the prior gradient is wrong exactly where it acts most strongly.","tokens_in":27389,"feed_emoji":"📡","tokens_out":9291,"duration_ms":80935,"temperature":0.7,"pith_summary":"The paper tries to establish that full-wave electromagnetic inverse scattering can be improved by injecting a learned score-based prior into the reconstruction while still enforcing the scattering physics through the Lippmann-Schwinger equations. ScoreField parameterizes the unknown permittivity contrast and the induced current field as two implicit neural representations, optimizes them jointly against the measured scattered field and the internal state equation, and uses a pretrained score model as a prior-gradient direction on the contrast. If correct, this gives a way to carry class-specific statistics into nonlinear multiple-scattering reconstructions without learning a fixed inverse map from data to image. The reported experiments on simulated strong- and weak-scattering targets, a ring-and-disk phantom, and measured microwave data show higher PSNR, SSIM, and MS-SSIM and lower LPIPS than the compared classical and learned solvers, including an average PSNR gain of about 1.8 dB over the best baseline on the real measured data.","feed_headline":"Score-based priors lift inverse scattering fidelity by 1.8 dB","feed_subtitle":"Coupled neural fields fold learned target statistics into full-wave reconstruction, cutting artifacts on real measured data.","key_machinery":"The load-bearing mechanism is the induced-current representation of the Lippmann-Schwinger model, discretized as $E=E^{\\mathrm{in}}+GJ$, $J=f\\odot E$, $y=SJ+e$, with $G$ the domain Green's operator and $S$ the receiver map. Two RFF-encoded SiLU MLPs realize the fields: the contrast INR $\\hat f_\\theta(r)$ maps spatial coordinates to bounded contrasts via a shifted $\\tanh$, and the current INR $\\hat J_\\eta(r;t)$ maps coordinates plus transmitter position to complex currents. The full-wave loss $L_{\\mathrm{phys}}=\\lambda_y L_{\\mathrm{data}}+\\lambda_s L_{\\mathrm{state}}$ couples the two INRs, and the score prior enters only through the contrast INR as $\\Delta^\\theta_{\\mathrm{score}}(k)=\\alpha_k(\\partial\\tilde f/\\partial\\theta)^* s_\\phi(\\tilde f,\\sigma_k)$, with noise scale and weight annealed by (26). Predicting $J$ instead of the internal scattered field keeps the receiver map linear in one INR and confines the nonlinear contrast-current coupling to the state residual.","core_discovery":"ScoreField claims that full-wave inverse scattering can be solved at test time by optimizing two coupled implicit neural representations under the Lippmann-Schwinger equations while a frozen score-based generative model supplies a learned prior gradient on the contrast. The contrast INR maps spatial coordinates to bounded contrasts, and the illumination-dependent current INR maps coordinates plus transmitter position to complex induced currents. A data loss on the scattered-field prediction and a state loss enforcing the self-consistent current relation couple the two networks, and the score prior is propagated to the contrast network through the adjoint Jacobian of the normalized contrast. On simulated strong- and weak-scattering benchmarks, a ring-and-disk phantom, and measured scattering data, the paper reports that this combination improves fidelity metrics and suppresses artifacts relative to classical full-wave solvers, plug-and-play denoisers, an INR-only solver, and a supervised U-Net backprojection baseline.","pith_inferences":["My inference: the same coupling should extend to three-dimensional, complex-valued-contrast inverse scattering, but the score model would need to be retrained in the appropriate normalized complex space, since the paper only demonstrates two-dimensional real-valued contrasts.","My inference: the annealing schedule itself is a testable dial; sweeping $\\sigma_{\\mathrm{min}}$ and $\\alpha_{\\mathrm{min}}$ should reveal a trade-off between prior strength and data fidelity that the current single-schedule experiments do not quantify.","My inference: comparing ScoreField's score-gradient update against a learned denoiser under the same full-wave data term isolates what score gradients buy beyond a generic learned denoiser; the reported gaps suggest the score formulation is the active ingredient, but an ablation with identical optimizer settings would confirm it.","My inference: the prior-mismatch robustness suggests the frozen score model could be reused for a different target class by rerunning the same reconstruction, potentially acting as a plug-and-play prior for electromagnetic and optical tomography, though this would need empirical confirmation."],"forward_implications":["In strong multiple-scattering settings, where first-Born linearization is inaccurate, the score prior should keep contrast estimates from drifting while the current INR tracks the self-consistent internal field.","On texture-rich target classes such as natural-face contrasts, ScoreField should reduce structured artifacts that total-variation and nonnegative baselines cannot suppress.","Because the score prior is pretrained on unpaired target-contrast images rather than paired measurement-target data, the prior generalizes across acquisition geometries and illuminations without retraining, as the same score model is used at both contrast scales.","A deliberately mismatched prior does not dominate the reconstruction; the full-wave data term continues to pull the estimate toward the measured target, as the ring-disk and measured-data trajectories show.","The reconstruction has a tunable calibration-fidelity tradeoff: enabling moderate dropout in the contrast INR lowers expected calibration error while keeping PSNR within roughly 0.3 dB of the deterministic run."],"supporting_citations":[{"why":"supplies the full-wave induced-current and state-loss formulation used here, as well as the LS-TV baseline.","marker":"[14]"},{"why":"provides the accelerated nonlinear diffractive imaging framework the optimizer builds on.","marker":"[15]"},{"why":"defines the ScaDec pipeline that the UNet-BP baseline follows for multiple-scattering inversion.","marker":"[18]"},{"why":"introduces coordinate-based implicit neural representations as continuous field parameterizations.","marker":"[19]"},{"why":"supplies the frozen random Fourier-feature encoding that lets the MLPs represent high-frequency contrast and currents.","marker":"[20]"},{"why":"is the INR-based Lippmann-Schwinger solver that ScoreField extends and evaluates against.","marker":"[21]"},{"why":"introduces denoising score matching, the training objective for the frozen score model.","marker":"[24]"},{"why":"gives the score-based generative framework that motivates using scores as prior gradients.","marker":"[26]"},{"why":"provides the attention U-Net architecture used to pretrain the score model.","marker":"[58]"},{"why":"supplies the measured experimental scattering data used in the real-data evaluation.","marker":"[59]"}],"fun_headline_variants":["Score priors lift inverse scattering by 1.8 dB","Coupled neural fields with score priors cut artifacts","Score-guided INRs solve full-wave inverse scattering","ScoreField: learned priors improve experimental reconstruction","Neural inversions with score-based priors: 1.8 dB gain"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"ScoreField's gains rest on the assumption that the frozen score model, evaluated on the normalized contrast estimate $\\tilde f$ at the annealing noise scales $\\sigma_k$, actually approximates the gradient of the log-density of the true target-contrast distribution; if that score is biased at the finest scales, the prior update can pull the reconstruction away from the measured scattered field.","fun_headline_variants_meta":{"raw":{"variants":["Score priors lift inverse scattering by 1.8 dB","Coupled neural fields with score priors cut artifacts","Score-guided INRs solve full-wave inverse scattering","ScoreField: learned priors improve experimental reconstruction","Neural inversions with score-based priors: 1.8 dB gain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1431,"prompt_tokens":923,"completion_tokens":508,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":426}},"tokens_in":539,"tokens_out":508,"duration_ms":5231,"temperature":1.0,"reasoning_tokens":426,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:54:55.534805+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Reconstruct a ring-and-disk phantom with a score model trained only on images that contain no disks or rings, and compare against the physics-only LS-TV baseline: if the score-guided run is not better, the claimed prior benefit is not robust to mismatch. Alternatively, estimate the true score at the chosen $\\sigma_{\\mathrm{min}}$ on held-out normalized contrasts and compare with $s_\\phi$; a large discrepancy there would mean the prior gradient is wrong exactly where it acts most strongly.","supporting_citations":[],"review_version":1}