Efficient Flow Matching for Sparse-View CT Reconstruction

Jiayang Shi^1,2, Lincen Yang¹, Zhong Li^1,3, Tristan van Leeuwen^2,4, Daniël M. Pelt¹, K. Joost Batenburg¹

¹LIACS, Leiden University ²Centrum Wiskunde & Informatica ³Great Bay University ⁴Mathematical Institute, Utrecht University

MICCAI 2026

arXiv Paper Code Pretrained Models

7–11

NFEs for EFMCT, versus 50–1000 for diffusion baselines

↓ 89%

fewer network evaluations than the most efficient diffusion method

↓ 78%

reconstruction time, at competitive PSNR / SSIM

0.83 s

per 512×512 slice on an RTX 4090 (AAPM)

Overview of the proposed FMCT (left) and EFMCT (right). FMCT integrates a pretrained flow matching ODE from noise $\bm{x}_1$ to a full-view CT image $\bm{x}_0$, and interleaves every Euler step with a physics-based data consistency correction. EFMCT reuses a previously predicted velocity field over several consecutive steps, so most steps cost no neural network evaluation at all; the small deviation this introduces is absorbed by the same data consistency correction.

Abstract

Generative models, particularly Diffusion Models (DM), have shown strong potential for Computed Tomography (CT) reconstruction serving as expressive priors for solving ill-posed inverse problems. However, diffusion-based reconstruction relies on Stochastic Differential Equations (SDEs) for forward diffusion and reverse denoising, where such stochasticity can interfere with repeated data consistency corrections in CT reconstruction. Since CT reconstruction is often time-critical in clinical and interventional scenarios, improving reconstruction efficiency is essential. In contrast, Flow Matching (FM) models sampling as a deterministic Ordinary Differential Equation (ODE), yielding smooth trajectories without stochastic noise injection. This deterministic formulation is naturally compatible with repeated data consistency operations. Furthermore, we observe that FM-predicted velocity fields exhibit strong correlations across adjacent steps. Motivated by this, we propose an FM-based CT reconstruction framework (FMCT) and an efficient variant (EFMCT) that reuses previously predicted velocity fields over consecutive steps to substantially reduce the number of Neural network Function Evaluations (NFEs), thereby improving inference efficiency. We provide theoretical analysis showing that the error introduced by velocity reuse is bounded when combined with data consistency operations. Extensive experiments demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. The codebase is open-sourced at github.com/EFMCT/EFMCT.

Contributions

To the best of our knowledge, the first flow-matching-based framework for CT reconstruction (FMCT).
A velocity field reuse strategy (EFMCT) that significantly improves the efficiency of FM-based CT reconstruction by reducing the required NFEs.
A proof that the single-step reuse error is of the same order as Euler discretization, and does not alter the overall convergence behavior under bounded consecutive reuse steps.
Extensive experiments demonstrating the reconstruction performance and efficiency of the proposed FM-based CT reconstruction method.

Motivation

Cosine similarity of consecutive velocity fields, and reconstruction quality versus NFE.

Left: cosine similarity of predicted velocity fields at consecutive iterations in FMCT, with and without data consistency correction, showing strong correlation across adjacent steps. Right: reconstruction performance vs. NFE for DM methods and FMCT/EFMCT, demonstrating that FMCT/EFMCT achieve competitive quality at substantially lower NFEs. DM methods here use the deterministic DDIM sampler for fairness; DPS/MCG results with the original 1000-step DDPM sampler are shown as isolated points. Results are averaged over the same randomly selected 21 reconstructions from the AAPM dataset across all iteration settings; shaded regions indicate standard deviation.

Diffusion solvers need a lot of iterations

Diffusion-based reconstruction models both the forward and the reverse process as an SDE. The repeated data consistency corrections that CT reconstruction requires interfere with that stochastic evolution, producing a push-and-pull effect between prior-driven denoising and physics-based correction. In practice this costs iterations: diffusion solvers typically need hundreds to thousands of NFEs.

Flow matching has better aligned steps

Flow matching instead transports probability mass deterministically along an ODE. Sampling follows a smooth trajectory with no noise injection, which interacts far more coherently with repeated data consistency corrections. Moreover, the velocity fields predicted along that trajectory stay almost perfectly aligned between neighbouring steps — the cosine similarity remains above 0.99 for nearly the entire trajectory, and stays that way even when a data consistency correction is applied in between. Re-evaluating the network at every single integration step is therefore largely redundant.

Method

FMCT: Flow Matching for CT Reconstruction

CT reconstruction recovers an object $\bm{x}\in\mathbb{R}^m$ from projections $\bm{y}=\bm{A}\bm{x}$, where $\bm{A}\in\mathbb{R}^{n\times m}$ is set by the acquisition geometry. In sparse-view CT, $n < m$, so the problem is underdetermined and ill-posed.

We use a conditional linear flow (Rectified Flow) trained on full-view CT images, so that $\bm{x}_t = (1-t)\bm{x}_0 + t\bm{x}_1$ with $\bm{x}_1\sim\mathcal{N}(\bm{0},\bm{I})$, and a network $\bm{v}_t^{\bm{\theta}}$ predicts the velocity. Given the pretrained model, each reconstruction step has three components.

1. Flow transport — an explicit Euler update along the learned velocity field:

$$\bm{x}_{t-\Delta t}^{\prime} = \bm{x}_t - \Delta t\,\bm{v}_t^{\bm{\theta}}(\bm{x}_t).$$

2. Data consistency — extrapolate to the terminal sample and refine it against the measurement (we use conjugate gradient, but the framework accepts any DC scheme):

$$\hat{\bm{x}}_0 = \bm{x}_t - t\,\bm{v}_t^{\bm{\theta}}(\bm{x}_t),\qquad \bm{v}_{\mathcal{DC}} = \mathcal{DC}(\hat{\bm{x}}_0, \bm{y}, \bm{A}).$$

3. Correction — apply the measurement-aware direction to the transported state:

$$\bm{x}_{t-\Delta t} = \bm{x}_{t-\Delta t}^{\prime} + \bm{v}_{\mathcal{DC}}.$$

These steps repeat until $t=0$ to give the final reconstruction.

EFMCT: Velocity Reuse for Efficient Sampling

Because consecutive velocities are nearly identical, EFMCT computes $\bm{v}_t = \bm{v}_t^{\bm{\theta}}(\bm{x}_t)$ once and reuses it for up to $M$ consecutive steps:

$$\bm{x}_{t-(j+1)\Delta t}^{\prime} = \bm{x}_{t-j\Delta t} - \Delta t\,\bm{v}_t, \qquad j\in[1, M].$$

Since $\bm{v}_t$ is reused without additional network evaluations, this directly reduces NFEs. To keep the sampler stable and data-faithful, an adaptive refinement check guards every reuse step:

$$\|\bm{A}\bm{x}_{t-(j+1)\Delta t}^{\prime} - \bm{y}\|^2 \;\leq\; \eta\,\|\bm{A}\bm{x}_{t-j\Delta t}^{\prime} - \bm{y}\|^2,$$

where $\eta > 1$ is a relaxation factor, empirically set to $\eta = 1.05$. If the condition is violated, reuse is terminated and the velocity is recomputed by the network. This mechanism balances efficiency against reconstruction accuracy.

Theory: the Reuse Error Is Bounded

Proposition 1. Assume $\bm{v}$ is locally Lipschitz in both $\bm{x}$ and $t$, i.e. $\|\bm{v}_t(\bm{x}) - \bm{v}_t(\bm{x}')\| \leq L_x\|\bm{x}-\bm{x}'\|$ and $\|\bm{v}_t(\bm{x}) - \bm{v}_{t'}(\bm{x})\| \leq L_t|t-t'|$ for all relevant $\bm{x}, \bm{x}', t, t'$. Then, for a single reuse step, the local deviation between the reuse update $\tilde{\bm{x}}_{k+1}$ and the standard Euler update $\bm{x}_{k+1}$ satisfies $\|\tilde{\bm{x}}_{k+1} - \bm{x}_{k+1}\| = \mathcal{O}(\Delta t^2)$, i.e. velocity reuse introduces a local error of the same order as the Euler discretization itself. Moreover, if the same velocity is reused for at most $M$ consecutive steps (independent of $\Delta t$) and the data-consistency correction is non-expansive with respect to its image argument, then the deviation remains controlled: the accumulated deviation after one reuse block is $\mathcal{O}(M^2\Delta t)$.

The proposition implies that velocity reuse introduces a local error of the same order as the Euler discretization itself. When the reuse length is bounded, the accumulated error remains controlled over consecutive reuse steps. The full proof is given in the appendix of the paper.

Results

We evaluate on two public datasets: the AAPM 2016 Low Dose CT Grand Challenge dataset (512×512, nine patients for training, patient L506 held out for testing) and the Medical Segmentation Decathlon CT dataset (Task_06 Lung, 512×512, ten patients for training, patient 017 for testing). Sparse-view measurements with 20 and 40 views are simulated with the ASTRA Toolbox under a parallel-beam geometry. Baselines are FBP, ADMM-TV, and four representative diffusion solvers: DPS, MCG, PGDM, and DDS.

Quantitative Comparison

Dataset	Method	40 views				20 views				NFE^*	Time / s
Dataset	Method	PSNR ↑	SSIM ↑	Data Fit ↓	LPIPS ↓	PSNR ↑	SSIM ↑	Data Fit ↓	LPIPS ↓	NFE^*	Time / s
AAPM	FBP	26.98±0.45	0.691±0.027	2783.64±233.30	0.391±0.014	24.01±0.49	0.547±0.029	1798.77±171.00	0.554±0.021	–	0.02
	ADMM-TV	31.94±0.42	0.836±0.027	22.11±2.29	0.272±0.027	29.45±0.46	0.798±0.029	17.53±2.00	0.380±0.028	–	9.85
	DPS	30.05±0.69	0.795±0.033	261.35±20.58	0.128±0.018	28.78±0.81	0.764±0.032	142.93±35.99	0.166±0.025	1000	142.16
	MCG	30.00±0.79	0.791±0.032	198.07±14.20	0.145±0.017	27.57±0.42	0.736±0.031	180.83±11.87	0.208±0.028	1000	143.44
	PGDM	30.26±0.61	0.803±0.030	208.98±13.72	0.159±0.022	29.43±0.60	0.775±0.031	106.51±5.30	0.187±0.025	100	29.79
	DDS	31.06±0.40	0.834±0.030	19.09±1.14	0.114±0.013	29.21±0.36	0.785±0.031	9.87±0.61	0.181±0.021	50	3.83
	FMCT (ours)	31.63±0.39	0.810±0.031	60.57±18.52	0.101±0.010	29.98±0.23	0.769±0.030	46.46±14.86	0.148±0.015	25 ↓50%	1.92 ↓50%
	EFMCT (ours)	31.52±0.28	0.832±0.027	182.80±104.39	0.129±0.014	29.52±0.23	0.795±0.027	111.41±79.80	0.194±0.021	7 ↓75%	0.83 ↓78%
Decathlon	FBP	28.01±0.76	0.763±0.037	2772.79±434.36	0.348±0.018	24.85±0.96	0.618±0.039	1731.97±305.77	0.512±0.026	–	0.02
	ADMM-TV	34.40±1.23	0.900±0.021	15.73±0.55	0.195±0.025	30.26±1.03	0.851±0.028	14.76±0.50	0.319±0.021	–	9.85
	DPS	33.85±1.25	0.870±0.018	250.11±18.61	0.128±0.037	31.69±1.44	0.842±0.025	121.25±18.57	0.140±0.038	1000	142.16
	MCG	30.03±1.20	0.824±0.030	301.17±35.25	0.164±0.034	28.67±1.26	0.798±0.038	198.22±22.68	0.186±0.026	1000	143.44
	PGDM	34.78±1.23	0.899±0.014	147.10±15.20	0.100±0.129	31.82±1.19	0.860±0.018	132.96±13.69	0.124±0.032	100	29.79
	DDS	37.66±1.20	0.923±0.009	15.10±9.29	0.072±0.015	33.00±1.29	0.873±0.018	5.01±0.36	0.110±0.017	100	7.65
	FMCT (ours)	37.65±1.53	0.912±0.020	334.44±74.21	0.109±0.021	33.41±1.57	0.841±0.036	294.97±58.87	0.180±0.026	50 ↓50%	4.09 ↓47%
	EFMCT (ours)	37.56±1.37	0.940±0.014	621.99±48.99	0.070±0.011	33.21±1.29	0.888±0.024	470.58±33.62	0.120±0.024	11 ↓89%	1.72 ↓78%

Mean and standard deviation are reported for PSNR, SSIM, data fidelity, and LPIPS (lower is better — LPIPS measures perceptual similarity to the reference). The best average result for each metric is shown in bold, and the second best is underlined. NFE^* counts only neural network forward evaluations. The percentages indicate the efficiency improvement in NFE and computation time (on an RTX 4090) of FMCT/EFMCT compared with the most efficient diffusion-based method. PSNR, SSIM and data fidelity are from Table 1 of the paper; LPIPS is from Table 2 in the appendix.

FMCT/EFMCT are often among the highest PSNR and SSIM across datasets and view configurations while requiring substantially fewer NFEs and lower computation time than diffusion-based baselines. ADMM-TV and DDS achieve the best and second-best data fidelity, reflecting their strong emphasis on measurement consistency. Compared with FMCT, EFMCT shows a slight reduction in PSNR and data fidelity but comparable or improved SSIM — with a significant efficiency improvement, down to 7 NFEs and 0.83 s per slice on AAPM. Perceptually, FMCT attains the best LPIPS on AAPM at both view counts, and EFMCT the best LPIPS on Decathlon at 40 views.

Visual Comparison

Visual comparison of reconstructions across different methods, datasets, and views. PSNR, SSIM, and reconstruction time are shown in the lower-left, lower-right, and upper-right corners of each image, respectively. We visualize only the best three diffusion-based methods for better visibility. Zoom in for more details (full-resolution PDF).

Sometimes ADMM-TV achieves the best PSNR/SSIM?

Although ADMM-TV achieves high PSNR/SSIM, its reconstructions are overly smooth and lack fine details. Diffusion-based methods and FMCT/EFMCT produce visually sharper and more detailed reconstructions, though they do not always exactly match the reference. This behavior is expected in sparse-view CT, where the problem is severely ill-posed and multiple reconstructions can satisfy the measurements. Generative methods balance data consistency with adherence to the learned prior, which may lead to small deviations in fine-scale details.

Ablation: When and How Much to Reuse

Ablation of the velocity reuse strategy. Left: reuse enabled after different iteration indices. Right: varying the maximum number of consecutive reuse steps. Shaded regions indicate standard deviation.

Both ablations use 21 randomly selected test CT images with the total number of sampling iterations fixed to 50.

When to start reusing

Fixing the maximum number of consecutive reuse steps to 10 and varying the iteration at which reuse is enabled, enabling reuse too early leads to an initial drop in reconstruction performance, whereas delaying reuse to later iterations gradually improves PSNR and SSIM. Early-stage sampling is more sensitive to approximation errors, while reuse becomes safer once the reconstruction has approached a more stable trajectory — velocity reuse is therefore better suited to mid- or late-stage sampling.

How long to reuse

Enabling reuse from the first iteration and varying the maximum number of allowed consecutive reuse steps, increasing the reuse limit initially improves PSNR and SSIM, indicating that moderate reuse does not adversely affect reconstruction quality. However, allowing excessive consecutive reuse degrades performance, revealing a trade-off between reconstruction quality and computational efficiency.

For all EFMCT results we adopt a reuse strategy that enables velocity reuse after the first iteration and allows up to 10 consecutive reuse steps.

Conclusion

We proposed FMCT/EFMCT, representing the first application of flow matching to CT reconstruction. By exploiting the deterministic transport structure of flow matching, we introduced a velocity reuse strategy that substantially reduces NFEs. We provided theoretical analysis showing that the error introduced by velocity reuse is of the same order as Euler discretization and remains bounded when combined with explicit data consistency operations. Extensive experiments on multiple datasets demonstrate that FMCT/EFMCT achieve competitive reconstruction quality while significantly improving computational efficiency compared with diffusion-based methods. We believe the proposed framework offers a practical and principled approach toward efficient generative CT reconstruction, with the potential to facilitate the deployment of advanced reconstruction methodologies in real-world clinical settings.

Code

The full codebase — training, reconstruction, and pretrained flow matching models for both datasets — is available at github.com/EFMCT/EFMCT. FMCT and EFMCT share a single reconstruction script; the two are selected purely by their sampling parameters:

Setting	num_inference_steps	skip_after	max_skips_in_a_row	eta ($\eta$)
FMCT (no velocity reuse)	50	50	any	any
EFMCT (velocity reuse)	50	0	10	1.05

For the diffusion-based comparison methods, please refer to the DM4CT benchmark repository.

Acknowledgements

The authors are supported by European Union H2020-MSCA-ITN-2020 under grant agreement no. 956172 and the Dutch Research Council under grant no. ENWSS.2018.003 and no. NWA.1160.18.316.

Disclosure of Interests. The authors have no competing interests to declare that are relevant to the content of this article.

BibTeX

@article{shi2026efficient,
  title={Efficient Flow Matching for Sparse-View {CT} Reconstruction},
  author={Shi, Jiayang and Yang, Lincen and Li, Zhong and van Leeuwen, Tristan
          and Pelt, Dani{\"e}l M. and Batenburg, K. Joost},
  journal={arXiv preprint arXiv:2603.00205},
  year={2026}
}