Cross-Distribution Diffusion CT Reconstruction

• The paper introduces a framework that alternates between a generative diffusion sampling step and a projection-consistency update to address ill-posed, sparse-view CT reconstruction under domain shifts.
• The method employs a scalable interpolant transformer with classifier-free guidance to integrate both domain-invariant and domain-specific image statistics for improved robustness.
• Empirical results demonstrate enhanced image quality metrics such as PSNR and SSIM across simulated and real datasets, outperforming traditional methods in OOD settings.

Cross-Distribution Diffusion Priors-Driven Iterative Reconstruction (CDPIR) is a sparse-view CT reconstruction framework designed specifically for out-of-distribution robustness. It combines a transformer-based diffusion prior learned across multiple datasets with model-based iterative reconstruction, and alternates between a generative sampling update and an explicit CT data-consistency update. In the formulation introduced in "Cross-Distribution Diffusion Priors-Driven Iterative Reconstruction for Sparse-View CT" (Li et al., 16 Sep 2025), the method targets scanner, protocol, geometry, and anatomy shifts that degrade single-distribution priors, and uses a Scalable Interpolant Transformer (SiT) with classifier-free guidance to couple domain-specific and domain-invariant image statistics.

1. Inverse-problem setting and motivation

CDPIR is formulated for sparse-view CT, where projection measurements are strongly undersampled and the reconstruction problem is ill-posed. The acquisition model is written as

$\mathbf{y} = \mathbf{A}\mathbf{x} + \epsilon,$

where $\mathbf{x} \in \mathbb{R}^n$ is the vectorized CT image, $\mathbf{y} \in \mathbb{R}^m$ is the vectorized sinogram, $\mathbf{A} \in \mathbb{R}^{m \times n}$ is the CT system matrix, and $\epsilon$ is additive noise. In sparse-view settings, typically $m<n$, so the forward operator alone does not determine a unique anatomically plausible solution (Li et al., 16 Sep 2025).

The framework is motivated not only by sparse-view ill-posedness but also by domain shift. The paper identifies scanner vendor and hardware, acquisition protocol, geometry, anatomy, and noise or reconstruction statistics as major sources of out-of-distribution degradation. It explicitly contrasts datasets such as AAPM and COCA to illustrate scanner, protocol, and anatomy shifts. Its central claim is that single-distribution generative priors are not robust enough for sparse-view CT under realistic domain shifts, and that reconstruction should therefore combine cross-distribution prior learning with explicit physics-based iterative correction (Li et al., 16 Sep 2025).

This positioning makes CDPIR a reconstruction framework rather than a pure generator. The diffusion model is not used as a standalone image synthesizer; it serves as a learned prior inside an alternating model-based solver. A plausible implication is that the method is aimed at regimes in which measurement incompleteness and prior mismatch are equally important failure modes.

2. Variational formulation and split reconstruction objective

The paper first states a constrained optimization problem,

$$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$

where $J(\mathbf{x})$ denotes the objective of the reverse diffusion process, $\|\nabla \mathbf{x}\|_1$ is total variation regularization, $\lambda_1$ controls the TV term, and $\mathbf{x} \in \mathbb{R}^n$0 is a noise tolerance. It then rewrites reconstruction as

$\mathbf{x} \in \mathbb{R}^n$1

which directly couples data fidelity, TV regularization, and the diffusion prior term (Li et al., 16 Sep 2025).

To make alternating optimization possible, the method introduces an auxiliary variable $\mathbf{x} \in \mathbb{R}^n$2 and imposes $\mathbf{x} \in \mathbb{R}^n$3: $\mathbf{x} \in \mathbb{R}^n$4 This yields two subproblems. The generative step is

$\mathbf{x} \in \mathbb{R}^n$5

which pulls the current iterate toward the learned image prior. The data-consistency step is

$\mathbf{x} \in \mathbb{R}^n$6

which enforces projection consistency while anchoring the reconstruction to the generative update (Li et al., 16 Sep 2025).

This split is central to the method’s identity. It is neither a pure posterior sampler nor a purely deterministic regularized inverse solver. Instead, it alternates a stochastic prior-imposing subproblem with a model-based image update.

3. Cross-distribution diffusion prior

The learned prior is built with a Scalable Interpolant Transformer. The paper places SiT inside a unified stochastic interpolant framework and uses a reverse-time process of the form

$\mathbf{x} \in \mathbb{R}^n$7

where $\mathbf{x} \in \mathbb{R}^n$8 is the velocity field and $\mathbf{x} \in \mathbb{R}^n$9 is the score function. The velocity is defined as

$\mathbf{y} \in \mathbb{R}^m$0

and the score is recovered from the velocity by

$\mathbf{y} \in \mathbb{R}^m$1

The paper presents this velocity-to-score mapping as the signature of its stochastic interpolant prior (Li et al., 16 Sep 2025).

The “cross-distribution” aspect is realized by multi-dataset training with classifier-free guidance. Each dataset is assigned a condition token $\mathbf{y} \in \mathbb{R}^m$2, and during training that token is randomly dropped and replaced by a null token $\mathbf{y} \in \mathbb{R}^m$3. At sampling time the guided velocity is

$\mathbf{y} \in \mathbb{R}^m$4

The paper then defines

$\mathbf{y} \in \mathbb{R}^m$5

so that

$\mathbf{y} \in \mathbb{R}^m$6

The null-conditioned branch is interpreted as domain-invariant and the residual as domain-specific; the paper does not present this as a hard disentanglement guarantee. In all reported experiments, $\mathbf{y} \in \mathbb{R}^m$7, so the practical effect of CFG is concentrated in the prior-learning structure rather than aggressive test-time amplification (Li et al., 16 Sep 2025).

Architecturally, the implementation uses SiT in the Big configuration, with patch size $\mathbf{y} \in \mathbb{R}^m$8, and removes the original autoencoder so that training and inference occur directly in the image domain. Table II reports CDPIR-B-2 with depth $\mathbf{y} \in \mathbb{R}^m$9, hidden size $\mathbf{A} \in \mathbb{R}^{m \times n}$0, attention heads $\mathbf{A} \in \mathbb{R}^{m \times n}$1, and $\mathbf{A} \in \mathbb{R}^{m \times n}$2M parameters, and CDPIR-S-2 with depth $\mathbf{A} \in \mathbb{R}^{m \times n}$3, hidden size $\mathbf{A} \in \mathbb{R}^{m \times n}$4, attention heads $\mathbf{A} \in \mathbb{R}^{m \times n}$5, and $\mathbf{A} \in \mathbb{R}^{m \times n}$6M parameters (Li et al., 16 Sep 2025).

4. Alternating reconstruction pipeline

Reconstruction begins with an ASD-POCS initialization obtained from the sparse-view data. The generative subproblem is then solved by a Stochastic Euler-Maruyama sampler based on the conditional VP-SDE diffusion transformer model. The data-consistency subproblem is handled by ASD-POCS with improved TV and Ordered-Subset SART, so the solver alternates between prior-imposing stochastic sampling and explicit projection-domain correction (Li et al., 16 Sep 2025).

The ASD-POCS update is written as a fusion of a SART step and a TV step: $\mathbf{A} \in \mathbb{R}^{m \times n}$7 where $\mathbf{A} \in \mathbb{R}^{m \times n}$8 is chosen adaptively so that

$\mathbf{A} \in \mathbb{R}^{m \times n}$9

This adaptive residual condition is intended to stabilize the data-consistency step by balancing projection fidelity against TV regularization (Li et al., 16 Sep 2025).

The guided score used in the SiT sampler is obtained from the guided velocity: $\epsilon$0 and the reverse process is

$\epsilon$1

The paper states that $\epsilon$2. It also states that inference uses $\epsilon$3 diffusion steps, with ASD-POCS outer iterations $\epsilon$4, TV inner iterations $\epsilon$5, subsets $\epsilon$6, and initialization-stage iterations $\epsilon$7 (Li et al., 16 Sep 2025).

Operationally, one alternating cycle can be summarized as follows. First, the current image estimate is updated by reverse-SDE sampling under the cross-distribution SiT prior. Second, the resulting image is corrected by ASD-POCS/iTV so that it better matches the measured sinogram. This alternating structure is the defining mechanics of CDPIR.

5. Empirical behavior under in-distribution and OOD conditions

The paper evaluates CDPIR on AAPM, COCA, XCAT, a real GE clinical cardiac dataset, and a MARS photon-counting CT extremity dataset, using PSNR and SSIM as the reported metrics. For simulation experiments on AAPM, COCA, and XCAT, full-view projections are numerically generated using GE clinical cardiac geometry through LEAP and then uniformly subsampled from $\epsilon$8 views to $\epsilon$9 views. For the GE clinical zero-shot evaluation, models trained on AAPM are tested on real GE clinical sparse-view sinograms with $m<n$0 views subsampled from $m<n$1. For MARS PCCT, each slice contains $m<n$2 views and is subsampled to $m<n$3 views (Li et al., 16 Sep 2025).

Quantitatively, CDPIR is reported as best or near-best across both in-distribution and OOD settings. In the strong OOD transfer from AAPM to COCA, it achieves $m<n$4 PSNR and $m<n$5 SSIM, compared with $m<n$6 and $m<n$7 for DDS. In the transfer from AAPM to XCAT, it achieves $m<n$8 and $m<n$9. When trained on COCA and tested on XCAT, it reaches $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$0 and $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$1. It also leads in-distribution, with $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$2 and $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$3 on AAPM trained and tested on AAPM, and $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$4 and $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$5 on COCA trained and tested on COCA (Li et al., 16 Sep 2025).

The ablations are aligned with the paper’s OOD thesis. Training on AAPM+COCA instead of AAPM alone improves OOD performance on XCAT from

$$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$6

to

$$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$7

Model scale also matters: on AAPM$$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$8COCA, CDPIR-S-2 gives $$\min_{\mathbf{x}} J(\mathbf{x}) + \lambda_1 \|\nabla \mathbf{x}\|_1, \qquad \text{s.t.} \qquad \|\mathbf{A}\mathbf{x} - \mathbf{y}\|_2^2 \le \delta_n,$$9, whereas CDPIR-B-2 gives $J(\mathbf{x})$0. The sampling-step study indicates that CDPIR reaches high-quality reconstructions with as few as $J(\mathbf{x})$1 steps, whereas DDS needs close to $J(\mathbf{x})$2 steps for comparable quality in the shown experiment (Li et al., 16 Sep 2025).

On real data, the paper reports that all baselines retain severe sparse-view artifacts on zero-shot GE clinical cardiac CT, while CDPIR suppresses them most effectively; the SSIM map suggests about $J(\mathbf{x})$3 over DDS. On far-OOD MARS PCCT wrist data, it is reported to improve over ASD-POCS by about $J(\mathbf{x})$4 dB PSNR and $J(\mathbf{x})$5 SSIM. These results are used to support the claim that CDPIR is robust not only to simulated domain shifts but also to real scanner and anatomy shifts (Li et al., 16 Sep 2025).

6. Position in diffusion-prior reconstruction literature and principal limitations

CDPIR belongs to a broader family of iterative inverse solvers that combine learned diffusion priors with explicit measurement operators. Earlier examples include "Diffusion Prior Regularized Iterative Reconstruction for Low-dose CT" (Xia et al., 2023), which alternates OS-SART with a DDPM prior; "DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction" (Du et al., 2024), which uses HQS to couple an INR data solver with a score-based prior and reports improved OOD behavior; "From Sparse X-rays to 3D CT: Training-Free Reconstruction with Diffusion Priors" (Zhang et al., 18 Jun 2026), which reuses a frozen voxel-space 3D Diffusion Transformer prior across X-ray-to-CT and several other medical inverse problems; "PET Image Reconstruction Using Deep Diffusion Image Prior" (Hashimoto et al., 20 Jul 2025), which adapts a diffusion prior across tracer and scanner shifts using Poisson-likelihood-guided fine-tuning; and "Steerable Conditional Diffusion for Domain Adaptation in PET Image Reconstruction" (Webber et al., 15 Oct 2025), which uses per-step LoRA adaptation to suppress hallucinated OOD artifacts. Relative to those methods, CDPIR’s distinctive move is to train the prior itself across multiple datasets and to interpret classifier-free guidance as a mechanism for coupling domain-invariant and domain-specific image statistics inside an alternating sparse-view CT solver (Li et al., 16 Sep 2025).

A more formal Bayesian precursor is "Score-Based Diffusion Models as Principled Priors for Inverse Imaging" (Feng et al., 2023), which turns score models into explicit densities through the probability flow ODE. CDPIR, by contrast, is an alternating model-based reconstruction method that uses a learned stochastic interpolant prior and ASD-POCS rather than explicit posterior optimization under an ODE-computed prior density. This suggests that CDPIR occupies a middle ground between explicit probabilistic prior modeling and engineering-oriented iterative reconstruction.

The paper also leaves several limitations explicit or implied. Inference is computationally heavy because it uses a large transformer and up to $J(\mathbf{x})$6 diffusion steps together with iterative ASD-POCS updates. The approach assumes access to multiple heterogeneous training datasets and meaningful domain labels. It introduces several balancing parameters and solver settings, including $J(\mathbf{x})$7, CFG scale, diffusion-step count, and ASD-POCS iteration structure, without a full sensitivity characterization. Finally, the exact SiT training loss and some sampling discretization details are not specified in the paper text provided, which makes full reproduction less direct (Li et al., 16 Sep 2025).

Taken together, CDPIR is best understood as a multi-domain generative-prior and physics-constrained reconstruction framework for sparse-view CT under domain shift. Its defining idea is that OOD robustness should not be assigned solely to stronger data consistency or solely to a broader diffusion model. Instead, it arises from the interaction of multi-distribution prior learning, null-conditioned and conditional guidance structure, transformer-based global modeling, and explicit iterative correction against the measured projections.