CvG-Diff: Cross-View Diffusion for Sparse CT

• The paper introduces a deterministic generalized diffusion framework that models actual FBP artifacts rather than synthetic Gaussian noise in sparse-view CT reconstruction.
• Error-Propagating Composite Training (EPCT) trains the network on intermediate states with propagated errors, resulting in a significant PSNR gain over baseline methods.
• Semantic-Prioritized Dual-Phase Sampling (SPDPS) decouples coarse anatomical correction from fine detail refinement to accelerate convergence and maintain high structural fidelity.

Cross-view Generalized Diffusion Model (CvG-Diff) is a sparse-view computed tomography reconstruction method that recasts sparse-view CT as a generalized, or “cold,” diffusion process driven by a deterministic degradation operator derived from the CT forward and reconstruction pipeline itself. Rather than modeling corruption as stochastic Gaussian noise, CvG-Diff models the actual image-domain artifacts induced by angular subsampling and filtered back-projection, and it exploits the observation that reconstructions produced from different numbers of projection views remain strongly correlated. In this formulation, reconstruction proceeds across a ladder of view counts, with two additional mechanisms—Error-Propagating Composite Training (EPCT) and Semantic-Prioritized Dual-Phase Sampling (SPDPS)—introduced to suppress error accumulation and reduce the number of sampling steps required in severe sparsity regimes (Chen et al., 14 Aug 2025).

1. Problem setting and meaning of “cross-view”

Sparse-view CT seeks to recover a diagnostic-quality image from a heavily undersampled set of projection angles. In standard filtered back-projection, angular undersampling produces severe streaking and structured aliasing artifacts. Supervised discriminative CNN and Transformer methods can learn one-step artifact suppression from paired sparse/full-view data, but in very sparse regimes they often oversmooth anatomy because large amounts of missing information must be inferred in a single pass. Conventional diffusion methods provide iterative refinement and strong image priors, yet the CvG-Diff paper identifies two mismatches between standard diffusion and sparse-view CT: the usual Gaussian corruption model does not match the deterministic artifacts created by angular subsampling, and long iterative chains can become unstable when the initial sparse-view reconstruction is extremely corrupted (Chen et al., 14 Aug 2025).

Within this context, “cross-view” does not denote multi-image joint input, neighboring-view fusion, or a dedicated angular attention module. The term refers instead to the structured relationship among reconstructions obtained from different numbers of views, such as $288, 234, 180, 126, 72, 54, 36,$ and $18$. These reconstructions share semantics and artifact structure, while denser-view reconstructions retain progressively more detail and fewer streaks. CvG-Diff uses these inter-level correlations to move iteratively from a sparse-view image toward cleaner reconstructions and ultimately to the full-view target.

The method is therefore positioned between one-step paired reconstruction and conventional stochastic diffusion. Its defining claim is that sparse-view CT is better modeled as inversion of a deterministic, physics-derived degradation path than as denoising of synthetic Gaussian perturbations. A common misconception is to treat CvG-Diff as a generic cross-view image generation model; in fact, its notion of view is specific to projection-count levels in CT reconstruction.

2. Generalized diffusion formulation

CvG-Diff adopts the generalized diffusion framework in which a clean image $x_0 \in \mathbb{R}^N$ is mapped to a degraded sample $x_t$ by a deterministic operator $D$: $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$ A restoration network $R_\theta$ is trained to predict the clean image directly: $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$ At inference, the reverse process alternates restoration and re-degradation. Given $x_t$, the network predicts

$\hat{x}_0^t = R_\theta(x_t, t),$

and updates to the next less degraded level via

$18$0

The final reconstruction is

$18$1

For sparse-view CT, the degradation operator is instantiated as

$18$2

where $18$3 is the Radon transform, $18$4 is a projection-domain subsampling mask at severity $18$5, and $18$6 is FBP reconstruction. The degraded sample is therefore the actual FBP image that would be obtained from a specified sparse-view acquisition, not a synthetically noised proxy.

The paper further defines a severity mapping $18$7 that assigns each diffusion level to a number of views from a predefined sequence

$18$8

This permits a single model to operate across multiple tested sparse-view settings. The importance of this formulation lies in its direct alignment with CT physics: each level corresponds to a concrete sampling pattern, and adjacent levels differ in artifact severity rather than in an abstract noise magnitude.

The paper also argues that a direct extension of generalized diffusion to this setting is insufficient because of artifact propagation. If an intermediate prediction $18$9 is inaccurate, the residual term $x_0 \in \mathbb{R}^N$0 carries structured errors forward, and the subsequent remapping to a denser level can accumulate new streaks that are not characteristic of the nominal degradation level. This motivates the two main additions of CvG-Diff.

3. Error-Propagating Composite Training

Error-Propagating Composite Training is the training mechanism used to reduce the train-test mismatch between ideal degraded states and the imperfect intermediate states encountered during multi-step inference. Naive generalized diffusion training exposes the network only to samples of the form $x_0 \in \mathbb{R}^N$1. Actual inference, however, produces states created by restoration-induced update rules, and those states can deviate substantially from the nominal degradation manifold once $x_0 \in \mathbb{R}^N$2 is imperfect.

EPCT addresses this mismatch by explicitly synthesizing intermediate states that contain propagated reconstruction errors. In each training iteration, the procedure first samples a target sparse-view level $x_0 \in \mathbb{R}^N$3, constructs $x_0 \in \mathbb{R}^N$4, and updates the restoration network with the basic loss. It then samples an intermediate level $x_0 \in \mathbb{R}^N$5, uses an EMA teacher network to obtain a more stable prediction, synthesizes a propagated-error state, and applies a second supervision step at the intermediate level. The core equations are

$x_0 \in \mathbb{R}^N$6

$x_0 \in \mathbb{R}^N$7

$x_0 \in \mathbb{R}^N$8

The EMA parameters are updated as

$x_0 \in \mathbb{R}^N$9

every $x_t$0 iterations.

The practical significance of EPCT is that the network is not trained solely on cleanly degraded sparse-view reconstructions; it is also trained on harder intermediate states whose errors resemble those generated by the reverse chain itself. The paper emphasizes that EPCT is the more important of the two proposed components. In ablation, adding EPCT to a baseline generalized diffusion model yields large gains across 18-view, 36-view, and 72-view settings, and the paper reports an average PSNR gain of $x_t$1 dB over the baseline (Chen et al., 14 Aug 2025).

This suggests that, in deterministic generalized diffusion for CT, robustness to self-induced distribution shift is at least as important as the choice of degradation operator itself. The method’s contribution is therefore not merely a new forward model, but a training protocol that teaches the network to recover from the specific error modes produced by iterative restoration.

4. Semantic-Prioritized Dual-Phase Sampling

SPDPS modifies inference rather than training. Its premise is that sparse-view CT reconstruction involves two distinct objectives that should not be treated identically throughout the reverse chain: first, recovering anatomically correct coarse structure and boundaries; second, refining high-frequency details. Sequential generalized diffusion can expend steps sharpening details around incorrect or blurred structures instead of correcting the semantic error itself.

The paper partitions the total number of sampling steps $x_t$2 into two phases,

$x_t$3

where the first $x_t$4 steps perform semantic correction and the final $x_t$5 steps perform detail refinement. In the reported configuration, $x_t$6. During the semantic phase, the method monitors consecutive clean-image predictions using SSIM: $x_t$7 When this criterion is satisfied, the method interprets it as anatomical convergence and performs an adaptive reset: $x_t$8 Rather than continuing from the current chain state, the reset reuses the original sparse-view observation $x_t$9 together with the improved estimate $D$0 to regenerate a better state at the next denser level. The paper states that SPDPS prioritizes “sparse-view level anatomical correctness before detail enhancement.”

This reset mechanism is central to CvG-Diff’s low-step sampling behavior. It uses the original sparse-view reconstruction as a reference for re-identifying error-prone regions, decouples semantic correction from detail sharpening, and avoids spending function evaluations on near-converged states. In the implementation reported for the AAPM-LDCT experiments, SPDPS uses $D$1 and $D$2 (Chen et al., 14 Aug 2025).

The ablation and sensitivity studies indicate that the reset threshold matters more than the exact number of detail-refinement steps. At 18-view, $D$3 yields $D$4 / $D$5, compared with $D$6 / $D$7 for $D$8 and $D$9 / $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$0 for $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$1. By contrast, varying $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$2 from $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$3 to $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$4 produces only minor differences. The paper’s interpretation is that early correction of blurred boundaries is the dominant factor.

A second common misconception is that SPDPS is a generic acceleration heuristic. In the CvG-Diff formulation it is more specific: it is an inference strategy designed to counteract the interaction between deterministic degradation, anatomical ambiguity at sparse levels, and structured artifact propagation.

5. Architecture, training pipeline, and empirical performance

The reconstruction backbone is a Diffusion UNet with residual blocks, following Cold Diffusion. The reported configuration uses a base feature dimension of $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$5, channel multipliers $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$6, and four resolution scales. The network takes an image-domain degraded reconstruction $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$7 together with its degradation level $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$8, and predicts the clean full-view image directly rather than a noise residual (Chen et al., 14 Aug 2025).

Experiments are conducted on the AAPM Low-Dose CT dataset with $x_t = D(x_0,t), \qquad D(x_0,0)=x_0.$9 slices from $R_\theta$0 patients. The train/validation portion contains $R_\theta$1 slices from $R_\theta$2 patients with a $R_\theta$3 split, and the test set contains $R_\theta$4 slices from $R_\theta$5 patient. Sparse-view projections are simulated in fan-beam geometry with TorchRadon / TorRadon, source-to-detector distance $R_\theta$6 cm, $R_\theta$7 detector elements, and scan parameters of $R_\theta$8 kVp and $R_\theta$9 mA. Target sparse-view settings are $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$0. Optimization uses $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$1 epochs, batch size $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$2, Adam with $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$3 and $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$4, initial learning rate $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$5, learning-rate decay by factor $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$6 after epoch $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$7, and EMA with $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$8 updated every $$\mathcal{L}_{\text{restore}} = \| R_\theta(D(x_0, t), t) - x_0 \|_2.$$9 iterations. Metrics are RMSE in HU, PSNR in dB, and SSIM.

The paper reports that CvG-Diff reaches high quality with very small numbers of function evaluations. The abstract states that on 18-view CT it achieves $x_t$0 dB PSNR and $x_t$1 SSIM using 10 steps. In the main quantitative table, the corresponding SSIM entry is reported as $x_t$2, while the runtime table reports $x_t$3 s for the 10-step setting and $x_t$4 s for a 6-step setting.

Setting	CvG-Diff result	Selected baseline comparison
18-view	38.34 dB / 95.18 SSIM (NFE=10)	DuDoTrans 34.02 dB / 90.12; VSS 32.34 dB / 87.90 (NFE=1000)
36-view	41.78 dB / 97.05 SSIM (NFE=10)	DuDoTrans 38.24 dB / 94.13; VSS 37.52 dB / 93.99
72-view	45.94 dB / 98.63 SSIM (NFE=10)	FreeSeed 42.93 dB / 97.53; VSS 41.92 dB / 97.07

Qualitatively, the paper reports that one-step methods tend to over-smooth structures, diffusion baselines can produce vivid-looking but lower-fidelity details under heavy sparsity, and CvG-Diff better preserves precise anatomical structures with smaller error maps. Runtime comparisons at 18-view are also reported: VSS with $x_t$5 NFE requires $x_t$6 s, CoSIGN with $x_t$7 NFE requires $x_t$8 s, CvG-Diff with $x_t$9 NFE requires $\hat{x}_0^t = R_\theta(x_t, t),$0 s, and CvG-Diff with $\hat{x}_0^t = R_\theta(x_t, t),$1 NFE requires $\hat{x}_0^t = R_\theta(x_t, t),$2 s.

The ablation study separates a deterministic generalized-diffusion baseline, baseline plus SPDPS, baseline plus EPCT, and the full model. For 18-view, these yield $\hat{x}_0^t = R_\theta(x_t, t),$3, $\hat{x}_0^t = R_\theta(x_t, t),$4, $\hat{x}_0^t = R_\theta(x_t, t),$5, and $\hat{x}_0^t = R_\theta(x_t, t),$6, respectively. Comparable trends are reported at 36-view and 72-view. This establishes that deterministic degradation alone is insufficient, SPDPS helps, and EPCT contributes the larger gain.

6. Position in the literature, distinctions, and limitations

CvG-Diff belongs to the cold/generalized diffusion line for inverse problems, where degradation is deterministic and problem-specific rather than Gaussian. A subsequent sparse-view CT paper, ReCo-Diff, explicitly positions itself as a refinement over CvG-Diff-style deterministic sampling. It adopts the same physics-based degradation operator and EPCT-style training, but critiques SSIM-based adaptive resets as heuristic and replaces them with residual-conditioned deterministic sampling based on image-space observation residuals computed through the degradation model (Choi et al., 3 Mar 2026). This later development indicates that CvG-Diff rapidly became a reference point for deterministic diffusion sampling in sparse-view CT, particularly in discussions of error accumulation and measurement-aware correction.

The term “cross-view” in CvG-Diff should also be distinguished from its use in cross-view image synthesis outside tomography. In satellite-to-street diffusion and geometry-guided satellite-ground synthesis, “cross-view” denotes large viewpoint changes between overhead and ground imagery and is handled through target-view structural controls, cross-view attention, or geometry-guided conditioning (Li et al., 2024); (Lin et al., 2024). CvG-Diff does not introduce such an explicit cross-view relational architecture. Its cross-view property is the unified modeling of CT reconstructions across a ladder of sparse angular sampling rates. A plausible implication is that the same label can describe substantially different technical ideas depending on the imaging domain.

More distant but conceptually related work on joint multimodal or shared-latent diffusion likewise differs in scope. Some methods emphasize a single shared denoiser over paired modalities through channel-wise conditioning (Hu et al., 2023), while others emphasize a modality-shared latent space with multiple decoders for aligned RGB+X generation (Wang et al., 2024). These approaches are relevant at the level of shared-structure modeling, but they do not supply the deterministic CT degradation operator that is central to CvG-Diff.

The CvG-Diff paper does not include a formal limitations section, but several constraints are explicit or evident in the reported setup. The method assumes a known deterministic CT degradation operator $\hat{x}_0^t = R_\theta(x_t, t),$7, so geometry and subsampling masks must be specified. The approach is image-domain only, and the authors explicitly suggest future work on dual-domain generalized diffusion that jointly optimizes sinogram and image-domain reconstruction. SPDPS depends on a hand-set SSIM threshold $\hat{x}_0^t = R_\theta(x_t, t),$8, and sensitivity experiments show that performance changes with this parameter. Cross-view levels are predefined by the schedule $\hat{x}_0^t = R_\theta(x_t, t),$9, so the choice of level ladder may affect performance. Although much faster than standard diffusion, the method remains multi-step and is therefore slower than the fastest single-pass discriminative networks. Finally, the reported experiments use AAPM-LDCT with simulated sparse views; the paper does not discuss real scanner deployment or mismatched acquisition settings (Chen et al., 14 Aug 2025).

Taken together, these features define CvG-Diff as a specialized deterministic diffusion framework for sparse-view CT rather than a generic denoising model. Its significance lies in the coupling of a physically meaningful degradation operator, training against propagated intermediate-state errors, and low-step sampling that prioritizes semantic correctness before detail enhancement.