Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction

Hualiang Wang; Jixiang Chen; Xiaomeng Li; Yi Qin; Yiqun Lin

REVIEW 3 major objections 6 minor 30 references

Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction

T0 review · 3 major / 6 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Sparse-view CT is rebuilt as a generalized diffusion process, reaching 38.34 dB PSNR from 18 views in 10 steps.

desk verdict 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. read the letter →

arxiv 2508.10313 v1 pith:FH72D656 submitted 2025-08-14 eess.IV

Jixiang Chen , Yiqun Lin , Yi Qin , Hualiang Wang , Xiaomeng Li This is my paper · ORCID

classification eess.IV

keywords Sparse-viewCTreconstructionDiffusionmodelGeneralizedDeterministicdegradationArtifactpropagationError-PropagatingCompositeTrainingSemantic-PrioritizedDual-PhaseSampling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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

What would settle it

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.

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Extended reading notes

Core claim

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

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

What'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.

The 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.

Overall, 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.

I 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.

Referee Report

3 major / 6 minor

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.

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 (3)

[§3.1, Table 1] 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.
[Table 1 vs. Introduction, Ref. [28]] 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.
[§2.3, Eq. (8), SPDPS] 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.

minor comments (6)

[§2.1, Eq. (4)] 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.
[Table 1] There is a typo in the VSS row: 'NEF=1000' should be 'NFE=1000'.
[Table 3] 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.
[Fig. 3, Fig. 4] The error maps would be easier to interpret if colorbars were included and the display windows for each row were stated in the captions.
[§2.2] 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.
[§3.1] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: empirical results are held-out and the degradation model is externally specified.

full rationale

The paper's central claim, quantified in Table 1, is an empirical comparison on a held-out patient of the AAPM-LDCT dataset. The model is trained with paired full-view and sparse-view data using the analytic degradation operator D(x0,T)=A†P(T)Ax0 (Eq. 4), which is defined from the Radon transform and FBP rather than from the target reconstruction. The training losses (Eq. 1 and Eq. 7) optimize the restoration network against ground-truth x0, so the testing numbers are not fitted parameters renamed as predictions. The generalized-diffusion update (Eq. 2) is taken from the external Cold Diffusion reference [1], not from the authors' own prior work. The same-group references (14-17) are cited only as related CT reconstruction methods and are not used to justify the load-bearing claim. The adaptive reset in Eq. 8 is an inference heuristic whose parameters tau and m are ablated in Table 3, not tuned on the test set. No uniqueness theorem or forced-choice argument is imported from the authors' prior work. The derivation chain is therefore self-contained: the deterministic degradation is physically specified, the network is trained on paired data, and the reported PSNR/SSIM are measured on held-out slices. Any concerns about statistical breadth or missing baselines are empirical-support issues, not circularity.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The central claim depends on hand-tuned hyperparameters (tau, m, N, T sequence) and on the unproven assumption that the deterministic cold-diffusion iteration converges for angular subsampling degradation. No new physical entities are introduced.

free parameters (5)

SSIM reset threshold tau = 0.97
Chosen by hand; Table 3 shows it affects 18-view PSNR by about 0.4 dB.
Detail refinement steps m = 4
Chosen by hand; Table 3 shows minor effect.
Total sampling steps N (NFE) = 6 or 10
Inference budget chosen by hand; the central claim uses N=10.
Severity level sequence T = [288, 234, 180, 126, 72, 54, 36, 18]
Hand-selected to cover target view counts; defines the degradation ladder for cross-view training.
EMA momentum gamma and update interval p = 0.995 and 10
Standard EMA hyperparameters; affect EPCT stability.

assumptions (3)

domain assumption The generalized diffusion reverse update Eq. (2) is a valid restoration step for arbitrary degradation operators.
Assumed from Cold Diffusion [1]; no convergence proof is given for this specific operator.
domain assumption Full-view FBP (A†A x0) is a valid clean target x0.
Boundary condition D(x0,0)=x0 holds only if the CT system is treated as invertible; in discrete fan-beam geometry A†A is an approximation, so x0 is defined as the FBP full-view reconstruction.
ad hoc to paper EMA network predictions are stable enough to simulate error propagation in EPCT.
Eq. (5)-(7) rely on EMA outputs as pseudo-labels; no justification of stability is provided.

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Cite this review

Pith. "Pith review of Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction." pith.science (2026). https://pith.science/paper/FH72D656

@misc{pith2026250810313,
  author       = {Pith},
  title        = {Pith review of: Cross-view Generalized Diffusion Model for Sparse-view CT Reconstruction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FH72D656}},
  note         = {Machine review of arXiv:2508.10313}
}

read the original abstract

Sparse-view computed tomography (CT) reduces radiation exposure by subsampling projection views, but conventional reconstruction methods produce severe streak artifacts with undersampled data. While deep-learning-based methods enable single-step artifact suppression, they often produce over-smoothed results under significant sparsity. Though diffusion models improve reconstruction via iterative refinement and generative priors, they require hundreds of sampling steps and struggle with stability in highly sparse regimes. To tackle these concerns, we present the Cross-view Generalized Diffusion Model (CvG-Diff), which reformulates sparse-view CT reconstruction as a generalized diffusion process. Unlike existing diffusion approaches that rely on stochastic Gaussian degradation, CvG-Diff explicitly models image-domain artifacts caused by angular subsampling as a deterministic degradation operator, leveraging correlations across sparse-view CT at different sample rates. To address the inherent artifact propagation and inefficiency of sequential sampling in generalized diffusion model, we introduce two innovations: Error-Propagating Composite Training (EPCT), which facilitates identifying error-prone regions and suppresses propagated artifacts, and Semantic-Prioritized Dual-Phase Sampling (SPDPS), an adaptive strategy that prioritizes semantic correctness before detail refinement. Together, these innovations enable CvG-Diff to achieve high-quality reconstructions with minimal iterations, achieving 38.34 dB PSNR and 0.9518 SSIM for 18-view CT using only \textbf{10} steps on AAPM-LDCT dataset. Extensive experiments demonstrate the superiority of CvG-Diff over state-of-the-art sparse-view CT reconstruction methods. The code is available at https://github.com/xmed-lab/CvG-Diff.

Figures

Figures reproduced from arXiv: 2508.10313 by the authors.

**Figure 1.** Overview of the proposed CvG-Diff. ite Training (EPCT) strategy, which simulates multi-step artifact accumulation during training to tackle propagated errors. Furthermore, we develop SemanticPrioritized Dual-Phase Sampling (SPDPS), a strategy that prioritizes anatomical correctness before detail refinement. It adaptively resets to input sparse-view level to leverage improved intermediate reconstructions in identif… view at source ↗

**Figure 2.** Error propagation issue in direct extension. Left: Incorrect reconstruction introduces streak artifacts. Right: Multi-step reconstruction results of performing I(xT , T). The model struggles to remove accumulated artifacts. provided it satisfies the boundary condition D(x0, 0) = x0, where x0 ∈ R N denotes the clean image. The forward process generates a degraded image xt at the severity level t via xt = D(x0, t). T… view at source ↗

**Figure 3.** Visual comparison of different methods. From top to bottom: Nv = {36, 72} with display windows [−1000, 2000], [−200, 300] HU, respectively. Red color in error maps indicate a larger error. 3.2 Comparison with State-of-The-Arts We evaluate CvG-Diff against two categories of state-of-the-art sparse-view CT reconstruction methods: (1) one-step feed-forward methods (FreeSeed [19], GloReDi [12], DuDoTrans [23]), which t… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: Visualization of multi-step reconstruction results between SPDPS (top) and sequential sampling (bottom). Error maps show deviations from ground truth (last column) in zoomed region, and red color indicates larger errors. The red box denotes the step when SPDPS resets t…

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Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [18]

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