{"id":"f4426b36-1f66-41f1-9032-7076fe9b76b5","arxiv_id":"2508.10313","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"CvG-Diff reformulates sparse-view CT reconstruction as a deterministic generalized diffusion process, achieving 38.34 dB PSNR for 18-view CT in 10 steps on AAPM-LDCT.","lead":"This paper introduces CvG-Diff, a diffusion-based method that reconstructs CT images from very few X-ray views by treating angular subsampling as a deterministic degradation process. It reports large quality gains over prior methods on a public low-dose CT dataset using only 10 sampling steps.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline metrics rest on one held-out patient with no error bars, and CT-SDM—the closest cited unified baseline—is absent from Table 1; the SOTA claim is not yet supported.","rationale":"The reader's weakest_assumption focuses on the lack of convergence analysis for the reverse update in Eq. (2). I agree that absence is real, but it is not the most load-bearing issue for the central claim: the method is an empirical reconstruction system, and the ablation study already demonstrates that EPCT and SPDPS improve the proposed pipeline in the tested setting. A missing theorem would not by itself overturn a well-supported empirical result. The more serious weakness is that the quantitative headline is computed over 526 slices from one test patient, with no error bars, and the most relevant unified baseline (CT-SDM) is omitted from the comparison. If the method's advantage shrinks or disappears under leave-one-patient-out evaluation, the claim that a single model can produce clinically useful images from 18 views in 10 steps loses its empirical foundation. My proposed check directly tests this. Since the reader's overall CONDITIONAL verdict already captures the need for more evidence, I would not change the verdict; I would only shift the emphasis from theoretical convergence to evaluation robustness and baseline completeness.","tokens_in":8756,"tokens_out":10495,"duration_ms":120750,"concrete_test":"Run a 10-fold leave-one-patient-out evaluation on AAPM-LDCT: for each of the 10 patients as test, train CvG-Diff on the other 9 (same fan-beam geometry, same view counts 18/36/72, same NFE=10), and report mean±std PSNR/SSIM over the 10 folds. In the same protocol, run CT-SDM [28] and the Table 1 baselines with identical preprocessing. If the 18-view PSNR across folds has a range greater than about 1.5 dB, or if CT-SDM is within 0.5 dB or outperforms CvG-Diff on any view count, the headline superiority claim should be substantially qualified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest claim is empirical: Table 1 reports 38.34 dB PSNR and 0.9518 SSIM at 18 views with NFE=10, outperforming one-step and diffusion baselines. The load-bearing evidence is narrow in two specific ways. First, Section 3.1 states the test set is 526 slices from a single patient; Table 1 reports a single mean with no per-patient spread or error bars. Since slices within a patient are highly correlated, this is effectively one independent test draw, so the headline number may not generalize. Second, the Introduction cites CT-SDM [28] as a unified sampling-diffusion model for sparse-view CT across sampling rates, but Table 1 never evaluates it, so 'superiority over state-of-the-art' is not tested against the closest recent baseline. The reverse update in Eq. (2) indeed lacks convergence analysis, but the architecture and training/inference design are coherent and the ablation in Table 2 supports the contributions; the limiting factor is the empirical support, not the missing theorem.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes CvG-Diff, a generalized diffusion model for sparse-view CT reconstruction. The method defines a deterministic degradation operator D(x0,T)=A^\\dagger P(T) A x0 that simulates angular subsampling and FBP artifacts, trains a restoration network across multiple sparsity levels, and introduces two components: Error-Propagating Composite Training (EPCT), which uses an EMA network to simulate multi-step artifact accumulation during training, and Semantic-Prioritized Dual-Phase Sampling (SPDPS), an adaptive inference strategy that resets the degradation level based on an SSIM convergence criterion. Experiments on AAPM-LDCT report 38.34 dB PSNR and 95.18% SSIM at 18 views with NFE=10, outperforming the tested one-step and diffusion baselines at 18/36/72 views, and ablations attribute the gains to EPCT and SPDPS. The code is publicly released.","tokens_in":9084,"tokens_out":7257,"duration_ms":77122,"significance":"If the empirical claims hold, the work is practically significant: it demonstrates that a physically grounded, deterministic degradation operator can replace Gaussian noise in a diffusion-style sampler for sparse-view CT, and that training against propagated artifacts (EPCT) plus an adaptive sampling schedule (SPDPS) yields strong reconstructions in very few network evaluations. The ablation study (Table 2) is well designed and cleanly isolates the contributions: EPCT provides a large average gain (about 3.8 dB), and SPDPS adds a smaller but consistent improvement. The explicit sensitivity analysis for tau and m (Table 3) and the public code release are also strengths. However, the headline claims rest on a narrow empirical base: a single test patient, no error bars, and the omission of the closest unified baseline (CT-SDM) from the comparison. These issues do not invalidate the method but currently prevent the paper from fully supporting its 'state-of-the-art' claim.","major_comments":[{"comment":"The test set is 526 slices from a single patient, and Table 1 reports only single mean values with no standard deviations or per-patient breakdown. Because neighboring slices from the same patient are highly correlated, this is effectively one independent evaluation draw. The headline numbers (38.34 dB PSNR, 95.18% SSIM at 18 views) and the claim of superiority over state-of-the-art methods are therefore not yet established across patients. Please evaluate on multiple held-out patients, or at minimum report per-patient ranges and error bars over slices/patients.","section":"§3.1, Table 1"},{"comment":"The Introduction cites CT-SDM as a unified sampling-diffusion model for sparse-view CT across sampling rates, which is the closest recent baseline to CvG-Diff's cross-view unified formulation. CT-SDM is not evaluated in Table 1, so the 'superiority over state-of-the-art' claim is not tested against the most relevant existing method. Please add CT-SDM (and ideally another recent unified model, e.g., Ref. [18]) to the comparison, or explicitly justify why it is excluded.","section":"Table 1 vs. Introduction, Ref. [28]"},{"comment":"The adaptive reset procedure is underspecified and the notation is ambiguous. After the criterion SSIM(hat x_t^0, hat x_{t+1}^0) > tau triggers at step t, Eq. (8) sets x'_{T-1} = x_T - D(hat x_t^0,T) + D(hat x_t^0,T-1), and the text says to perform I(x'_{T-1}, T-1). However, I(.,.) was defined in §2.1 as a full sequential schedule from the given level down to level 1, and the reset jumps to T-1 regardless of the current t. It is unclear how this is consistent with the 'n steps' budget of the semantic-correction phase, how many network evaluations a reset consumes, and what happens if the criterion triggers multiple times. A precise pseudocode with an exact NFE count is needed for reproducibility.","section":"§2.3, Eq. (8), SPDPS"}],"minor_comments":[{"comment":"The notation T is overloaded: it is used both as a severity level index and as a number of views in P(T). Please define the mapping g(t) and consistently write P(T_t) (or similar) to remove ambiguity.","section":"§2.1, Eq. (4)"},{"comment":"There is a typo in the VSS row: 'NEF=1000' should be 'NFE=1000'.","section":"Table 1"},{"comment":"The sensitivity analysis for tau and m is reported only for 18-view. Reporting the same analysis for 36-view and 72-view would strengthen the claim that SPDPS is robust across sparsity levels.","section":"Table 3"},{"comment":"The error maps would be easier to interpret if colorbars were included and the display windows for each row were stated in the captions.","section":"Fig. 3, Fig. 4"},{"comment":"The paper does not analyze whether the reverse update in Eq. (2) converges for the deterministic degradation operator. This absence is not fatal given the empirical ablation, but it should be explicitly acknowledged as a limitation rather than implied.","section":"§2.2"},{"comment":"Please specify the full-view reference (number of projections used for the 'full-view' images) and state whether all baseline methods use the same TorRadon simulation and the same preprocessing.","section":"§3.1"}],"recommendation":"major_revision","confidential_remarks":"The paper's self-citations (refs 14-17) are prior CT reconstruction works and do not raise circularity concerns. The main risk is empirical breadth: single-patient testing and the missing CT-SDM baseline. The ablation and code release are positive signals, and the method appears defensible if the comparison and statistical support are strengthened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The headline: this is a solid, well-engineered adaptation of Cold Diffusion to sparse-view CT, and the two proposed components—EPCT and SPDPS—are real improvements, validated by a clean ablation. The main thing holding the paper back is the narrow evaluation: one test patient, no error bars, and the closest cited unified baseline (CT-SDM) is missing from the comparison table.\n\nWhat's actually new: the deterministic degradation operator D(x0,T)=A†P(T)Ax0 is the natural way to model angular subsampling in a diffusion framework, and the cross-view training across a ladder of view counts is a useful idea. EPCT, which trains the network on artifacts propagated from coarser to finer levels, gives a 3.80 dB average gain over the baseline in Table 2. That's a big, credible improvement. SPDPS adds a smaller but consistent gain, and the visualization in Fig. 4 shows it corrects a real failure mode of sequential sampling. The code is released, which makes the results reproducible.\n\nThe soft spots are mostly in the evidence, not the method. Table 1 reports a single mean per metric per view count, with no standard deviation, and the test set is 526 slices from one patient. Since slices within a patient are highly correlated, the effective test size is close to one independent draw. That means the 38.34 dB PSNR figure is a point estimate without a confidence interval, and the claim of 'superiority over state-of-the-art' is not yet supported against the closest recent baseline: CT-SDM is cited in the introduction but never evaluated. Also, the hyperparameters τ and m are tuned without a reported validation protocol, so there is some selection risk. The absence of convergence analysis for the reverse update in Eq. (2) is a real gap, but it is not the limiting factor for this paper; the empirical evaluation is.\n\nOverall, this is a serious piece of work. The method is sensible, the ablations back up the design choices, and the deterministic degradation operator is physically appropriate. The paper needs a stronger evaluation before the SOTA claim is accepted: multiple test patients, per-patient variance, and a comparison with CT-SDM. With those additions, it could be a useful contribution to the sparse-view CT literature.\n\nI would send it to peer review. It deserves referee time, and the authors have shown they can run a proper ablation; the missing baselines and statistical rigor are fixable in revision.","headline":"Solid Cold Diffusion adaptation for sparse-view CT with genuinely useful training and sampling tricks, but the SOTA claim rests on a single-patient, no-error-bar evaluation and a missing CT-SDM baseline.","tokens_in":9484,"tokens_out":2254,"would_cite":true,"duration_ms":23759,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Sparse-view CT is rebuilt as a generalized diffusion process, reaching 38.34 dB PSNR from 18 views in 10 steps.","keywords":["Sparse-view CT","CT reconstruction","Diffusion model","Generalized diffusion","Deterministic degradation","Artifact propagation","Error-Propagating Composite Training","Semantic-Prioritized Dual-Phase Sampling"],"falsifier":"Run the trained model on a held-out patient slice and compute RMSE between $\\hat{x}_0^t$ and ground truth after every reverse step without SPDPS; if RMSE increases at any intermediate severity level, the sequential update is not a convergent refinement. Equivalently, feed real measured 18-view sinograms with photon noise into the model: if the PSNR drop relative to the clean simulated case is large, the deterministic operator $A^{\\dagger}P(t)A$ does not capture the true degradation the paper claims to model.","tokens_in":8702,"feed_emoji":"🩻","tokens_out":9237,"duration_ms":88041,"temperature":0.7,"pith_summary":"These authors are trying to establish that sparse-view CT reconstruction can be cast as a generalized diffusion process whose degradation is not Gaussian noise but the actual streak artifacts produced by skipping projection views. If the claim holds, a single trained model can reconstruct clinically useful CT images from as few as 18 views in about ten refinement steps, rather than the hundreds of steps standard diffusion solvers require. Two mechanisms carry the argument: Error-Propagating Composite Training (EPCT), which simulates multi-step artifact accumulation so the network learns to correct propagated streaks, and Semantic-Prioritized Dual-Phase Sampling (SPDPS), which locks in correct anatomy before refining details. On the AAPM-LDCT dataset the method reports 38.34 dB PSNR and 0.9518 SSIM at 18 views and outperforms both one-step artifact-removal networks and multi-step diffusion baselines at 18, 36, and 72 views.","feed_headline":"CT from 18 views in 10 steps at 38.34 dB PSNR","feed_subtitle":"One generalized diffusion model handles 18, 36, and 72 views by treating undersampling artifacts as deterministic degradation.","key_machinery":"The load-bearing object is the deterministic degradation operator $D(x_0,t)=A^{\\dagger}P(t)Ax_0$, whose role is to put different angular sampling rates on one severity ladder so a single restoration network can be trained across them. The reverse update $x_{t-1}=x_t-D(\\hat{x}_0^t,t)+D(\\hat{x}_0^t,t-1)$ applies that operator to each intermediate estimate and keeps the estimate consistent with the measured projections. EPCT is the training mechanism that injects simulated multi-step artifacts into the student network via an EMA teacher, and SPDPS is the inference mechanism that decides when to jump back to a sparser level based on an SSIM threshold, so that anatomical correctness is establishe","core_discovery":"The central claim is that angular subsampling artifacts form a deterministic degradation operator $D(x_0,t)=A^{\\dagger}P(t)Ax_0$---forward Radon transform $A$, angular subsampling mask $P(t)$, filtered back-projection $A^{\\dagger}$---and that a network $R_\\theta$ trained to invert this operator can reconstruct the full-view image through the reverse update $x_{t-1}=x_t-D(\\hat{x}_0^t,t)+D(\\hat{x}_0^t,t-1)$. Training only with the basic restoration loss leaves the network unable to fix errors that accumulate across steps, so the authors add EPCT: an EMA teacher generates a reconstruction at level $T$, re-degrades it to an intermediate level $t$, and the student is trained to restore that compo","pith_inferences":["Beyond the paper's claims, the same severity-ladder construction should transfer to any inverse problem with a deterministic undersampling operator---radial MRI, electron tomography, deblurring---where one model could be trained to invert a ladder of physical degradations in a few steps.","A testable extension is to replace the hand-chosen view ladder and SSIM reset threshold with a learned or uncertainty-driven schedule, which could remove the two hyperparameters the method currently depends on.","The experiments use simulated clean fan-beam projections on one dataset; whether the deterministic operator remains faithful under real scanner geometry, photon noise, and metal artifacts is an open question that measured sparse-view sinograms would answer.","The view-ladder design suggests a natural curriculum: train on denser views first and sparse views later, so the EMA teacher's composite inputs are themselves increasingly realistic; the current training samples levels uniformly at random."],"forward_implications":["A single network trained on the view ladder $[288,234,180,126,72,54,36,18]$ serves all three target sparsity levels without per-level retraining.","Ten network evaluations are enough: 18-view PSNR/SSIM reach 38.34 dB/0.9518, 36-view 41.78 dB/0.9705, and 72-view 45.94 dB/0.9863, with 0.68 s inference time.","EPCT is the main driver: adding it yields about a 3.80 dB averaged PSNR improvement over the generalized-diffusion baseline in the ablation study.","SPDPS improves anatomical boundary recovery by resetting the degradation level when successive reconstructions are similar, and the SSIM threshold $\\tau$ matters more than the number of refinement steps $m$ in the tested range.","CvG-Diff claims superior or matching performance against one-step feed-forward methods and multi-step diffusion methods at every tested view count, while using far fewer steps than the 1000-step diffusion baseline.","Because the method needs only 10 steps, it opens a practical route for iterative sparse-view CT reconstruction at near-real-time speeds."],"supporting_citations":[{"why":"Supplies the generalized diffusion formulation: an arbitrary degradation operator $D$ with boundary condition $D(x_0,0)=x_0$ and a restoration operator trained to invert it.","marker":"[1]"},{"why":"Provides the AAPM Low-Dose CT dataset of 5,936 slices from 10 patients that the method is trained and evaluated on.","marker":"[20]"},{"why":"Supplies the differentiable fan-beam projection and back-projection routines used to simulate sparse-view sinograms and filtered back-projections.","marker":"[22]"},{"why":"Zero-shot variational score solver, the multi-step diffusion baseline that requires 1000 sampling steps and is compared against in the experiments.","marker":"[8]"},{"why":"CoSIGN consistency-model few-step guidance, the few-step diffusion baseline compared at NFEs of 1 and 10.","marker":"[30]"},{"why":"GloReDi, a one-step feed-forward baseline using global representation distillation, included in the comparison table.","marker":"[12]"},{"why":"FreeSeed, a one-step frequency-band-aware and self-guided baseline used in the comparison table.","marker":"[19]"},{"why":"DuDoTrans, a one-step dual-domain transformer baseline used in the comparison table.","marker":"[23]"}],"fun_headline_variants":["10-step sparse CT hits 38 dB PSNR","Cross-view diffusion fixes sparse CT in 10 steps","Sparse CT: one model, 3 views, 10 steps","Deterministic degradation unfolds CT from 18 views","Fast sparse CT: 10 steps to 38 dB PSNR"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that the reverse update $x_{t-1}=x_t-D(\\hat{x}_0^t,t)+D(\\hat{x}_0^t,t-1)$ repeated over the hand-chosen severity ladder is a convergent refinement for $D(x_0,T)=A^{\\dagger}P(T)Ax_0$; the paper offers no theorem or convergence analysis for this iteration, and its success rests on the empirical EPCT/SPDPS combination validated on one simulated dataset.","fun_headline_variants_meta":{"raw":{"variants":["10-step sparse CT hits 38 dB PSNR","Cross-view diffusion fixes sparse CT in 10 steps","Sparse CT: one model, 3 views, 10 steps","Deterministic degradation unfolds CT from 18 views","Fast sparse CT: 10 steps to 38 dB PSNR"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000164,"raw_usage":{"total_tokens":1142,"prompt_tokens":862,"completion_tokens":280,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":606,"completion_tokens_details":{"reasoning_tokens":195}},"tokens_in":606,"tokens_out":280,"duration_ms":3041,"temperature":1.0,"reasoning_tokens":195,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T20:30:43.837237+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the trained model on a held-out patient slice and compute RMSE between $\\hat{x}_0^t$ and ground truth after every reverse step without SPDPS; if RMSE increases at any intermediate severity level, the sequential update is not a convergent refinement. Equivalently, feed real measured 18-view sinograms with photon noise into the model: if the PSNR drop relative to the clean simulated case is large, the deterministic operator $A^{\\dagger}P(t)A$ does not capture the true degradation the paper claims to model.","supporting_citations":[{"cited_title":"Advances in Neural Information Processing Systems 36, 41259– 41282 (2023)","cited_arxiv_id":null,"evidence_quote":"Supplies the generalized diffusion formulation: an arbitrary degradation operator $D$ with boundary condition $D(x_0,0)=x_0$ and a restoration operator trained to invert it."},{"cited_title":"Med- ical physics 43(6Part35), 3759–3760 (2016)","cited_arxiv_id":null,"evidence_quote":"Provides the AAPM Low-Dose CT dataset of 5,936 slices from 10 patients that the method is trained and evaluated on."},{"cited_title":"IEEE Transactions on Medical Imaging (2024) 10 F","cited_arxiv_id":null,"evidence_quote":"Zero-shot variational score solver, the multi-step diffusion baseline that requires 1000 sampling steps and is compared against in the experiments."},{"cited_title":"In: European Conference on Computer Vision","cited_arxiv_id":null,"evidence_quote":"CoSIGN consistency-model few-step guidance, the few-step diffusion baseline compared at NFEs of 1 and 10."},{"cited_title":"In: Proceedings of the IEEE/CVF International Conference on Computer Vision","cited_arxiv_id":null,"evidence_quote":"GloReDi, a one-step feed-forward baseline using global representation distillation, included in the comparison table."},{"cited_title":"In: International Conference on Medical Image Computing and Computer-Assisted Intervention","cited_arxiv_id":null,"evidence_quote":"FreeSeed, a one-step frequency-band-aware and self-guided baseline used in the comparison table."},{"cited_title":"In: International Workshop on Machine Learning for Medical Image Reconstruction","cited_arxiv_id":null,"evidence_quote":"DuDoTrans, a one-step dual-domain transformer baseline used in the comparison table."}],"review_version":1}