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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 https://github.com/EFMCT/EFMCT.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/3850_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/EFMCT/EFMCT
Link to the Dataset(s)
N/A
BibTex
@InProceedings{ShiJia_Efficient_MICCAI2026,
author = { Shi, Jiayang AND Yang, Lincen AND Li, Zhong AND van Leeuwen, Tristan AND Pelt, Daniël M. AND Batenburg, K. Joost},
title = { { Efficient Flow Matching for Sparse-View CT Reconstruction } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16888},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The proposed paper presents an accelerated flow matching framework with an application to sparse-view CT reconstruction. Flow-matching for CT (FMCT) uses a trained velocity v (a neural network) to sample an image from pure noise by iteratively solving an ODE with the trained velocity v. This framework can be used to solve an inverse problem by adding a data consistency (DC) update at each iteration. The problem is that this approach requires many evaluations of v, which is computationally expensive. The authors noticed experimentally that the velocity v does not change much after each iteration and therefore propose to reuse the same v for M iterations. Under basic regularity conditions on v, the approximate trajectory obtained by recycling the same velocity is expected not to deviate significantly from the trajectory obtained by reevaluating v at each iteration.
The authors demonstrate that their method Efficient FMCT (EFMCT) achieves similar image quality with much fewer neural network function evaluations (NFE).
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
This is a novel and well-motivated approach that could become an important direction for flow-matching-based CT reconstruction, especially in the case of large volumes where computational cost is critical.
The idea of reusing the velocity field is simple yet effective, and the empirical observation that consecutive velocities are similar is convincing. The method has strong practical relevance and the experimental results support the claimed efficiency gains.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
It seems to me that there is a problem in the proof. The current proof is based on an update of the form x_{k+1} = DC(x_k - Delta t v_tk (x_tk)) and xhat_{k+1} = DC(x_k - Delta t v_tk0 (x_tk0)) with DC kappa-non-expansive.
However, the update defined in (6) and (7) is x_{k+1} = x’_k+1 + DC(x_tk - tk v_tk(x_tk)) with x’_k+1 = x_k - Delta t v_tk (x_tk).
With this model, the error |delta_k+1| is bounded by (kappa + 1) |delta_k| + (tk*kappa + Delta t) | v_tk - v_tk0 |.
With this upper bound, I find that |delta_k0+M| is O(Delta t) and not O(Delta t^2).
The authors should carefully re-examine the proof and modify the statement if necessary.
Minor
-
There is a notation clash between xhat_0 (the expected non-noisy image E(x0 | x1)) and xhat_k (the alternative algorithm).
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The Euler scheme in the single step error part corresponds to the image-to-noise ODE, while the rest of the paper considers sampling from noise to image. This should be clarified.
-
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The method seems to work and can potentially drastically speed up FM reconstruction in CT, especially for large volumes.
However, there might be an issue in the proof. The authors should check it carefully, make the relevant modifications, and adjust their claims if necessary.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
I was already satisfied with this paper, and my only concern was the issue in the proof (cf. Q7). I have no more concern regarding the paper now that the authors have promised they will amend the proof in the final version of the paper.
Review #2
- Please describe the contribution of the paper
This paper proposes a novel CT reconstruction method based on flow matching. Unlike conventional diffusion models, flow matching enables deterministic sampling through an ODE-based formulation. Building on this property, the paper aims to reduce the NFEs by reusing gradients across adjacent sampling steps. The experimental results show that gradient reuse can effectively reduce NFEs while achieving better performance than the baseline methods.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.This paper proposes a diffusion-based solver for CT reconstruction based on the flow matching method. 2.By leveraging the deterministic nature of flow matching, the paper demonstrates the similarity of velocities between adjacent steps and proposes reusing gradients across neighboring steps to reduce the NFEs, thereby accelerating CT reconstruction. 3.The paper further proposes an adaptive and efficient flow matching sampling strategy based on the data-fidelity error across adjacent iterative steps, in order to further reduce the NFEs.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
I particularly like the paper’s proposed strategy for reducing NFEs, as it is both intuitive and well motivated. However, I believe the manuscript still has the following issues:
1.In the left panel of Fig. 1, why does the similarity exhibit a noticeable drop near 50 steps? The paper does not seem to provide an explanation for this phenomenon. 2.Does the central assumption of the proposed method still hold when Poisson noise is introduced? 3.From a clinical perspective, fan-beam geometry is more realistic than parallel-beam geometry. In addition, the visualization results do not indicate the HU window settings. I recommend that the authors present the images with appropriate windowing so that finer structural differences can be more clearly revealed. 4.The baselines selected by the authors are relatively old and were not specifically designed for CT reconstruction. The manuscript does not include more recent diffusion-based sampling or reconstruction methods developed specifically for CT reconstruction. I encourage the authors to refer to relevant studies published in recent years in venues such as MICCAI and journals such as TMI. 5.The paper does not provide sufficient training details for the flow matching model. Moreover, some of the compared methods, such as DPS and MCG, are originally built upon diffusion models rather than flow matching models. This raises a potential concern about the fairness of the comparison.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
1.Why do the authors use the conjugate gradient method to enforce data consistency? Why not directly adopt an (L_2) or (L_1) norm formulation?
2.Have the authors attempted to apply gradient reuse to diffusion models as well? In diffusion models, the gradients in the middle and late stages are also relatively stable.
3.The authors may consider including perceptual metrics, such as LPIPS, which could better reflect the ability of different methods to preserve fine details, for example when comparing ADMM-TV and EFMCT.
If the authors can adequately address these weaknesses and concerns, I would be willing to raise my score.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The method proposed in this paper is interesting; however, the experimental evaluation is not sufficiently rigorous.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The authors have addressed my concerns.
Review #3
- Please describe the contribution of the paper
The paper introduces a method for sparse-view CT reconstruction using flow matching models. First, flow matching is used to learn a velocity field that transforms Gaussian noise into CT images. Then, the sampling process is incorporated with data consistency operators to sample CT images conditioned on the observed measurements. A velocity reuse technique is proposed to accelerate inference, with theoretical analysis showing that the error remains first-order under the reuse. Results show competitive accuracy and improved speed of the proposed method.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The motivation of accelerating CT reconstruction is convincing and potentially useful for clinical practice. 2.The authors attempted to provide theoretical guarantees for their proposed method, which is essential for its reliable use and often neglected in the field.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.The theoretical statement is relatively unclear. Some notations are not consistently defined, and the proof appears to omit important steps. Specifically, it is unclear why the bounds on $| \delta_{k+1}|$ and $| \delta_{k_0 + M}|$ hold. The update rule for $\hat{x}_k$ lacks a formal definition, and it is unclear whether the refinement step in (9) is used. Similarly, $x_k$ is defined without the DC operator, but later seemed to denote iterates that include it. The bounded velocity is used but not stated as an assumption. Overall, the proposition and its proof appear too compressed and hard to follow in the current form. 2.Additionally, a formal description of the DC operator is missing, except that it uses conjugate gradient. What problem does it solve? How does it enforce or enhance data consistency? The authors may want to clarify on this in more details.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission has provided an anonymized link to the source code, dataset, or any other dependencies.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The proposed method is well-motivated and empirically validated. Although the theoretical results appear reasonable, the clarity of assumptions, notations, and the proof can be significantly improved.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Reject
- [Post rebuttal] Please justify your final decision from above.
The issues with the proof remain: 1.\hat{x}_k lacks a formal definition. 2.x_k is defined without the DC step (ie for unconditional sampling), but its seems to represent the iterates involving DC. This may have contributed to the confusion on how DC is applied. The authors’ rebuttal attempts to explain in words how the proof will be fixed, but the explanation itself is somewhat unclear and lacks the precision and rigor of mathematical terms. Unfortunately, it’s not fully convincing to me. Although it’s very valuable to see a formal guarantee on the method, the way it’s currently presented falls short of the standard for publication.
Author Feedback
We thank all reviewers for their positive assessment (novelty, motivation, practical relevance) and constructive feedback. We address the concerns below.
Issues in proof(R1R3) We carefully re-examined the proof and agree there was a discrepancy between the theoretical formulation and the actual update rule. The previous proof modeled the DC step on the current state, while the actual algorithm applies DC to the estimated clean image. We revised the proof by: 1)unifying notation (x̃) for the reuse trajectory, 2)consistently using the reverse noise-to-image ODE, and 3)explicitly modeling DC on the estimated clean image. The single-step bound remains O(Δt²), matching Euler local truncation error, while the accumulated deviation over one reuse block becomes O(M²Δt), rather than O(M²Δt²). We corrected the proposition and adjusted the claims accordingly. The complete proof will be released in the public repository.
DC operation(R2R3) We use conjugate gradient [Fletcher 1964] as the DC operation because it efficiently solves the least-squares problem (AᵀA+γI)x=x̂₀+Aᵀy. Compared with directly injecting L1/L2 gradients into the generative process, the decoupled optimization is less sensitive to delicate guidance-step tuning since DC refinement is separated from generative transport dynamics.
Choice of baselines/lack of CT-specific methods(R2) Our goal is not to outperform every recent CT-specific diffusion variant, but to investigate whether flow matching can serve as an efficient alternative to diffusion-based solvers. We therefore selected representative baselines covering different DC strategies: DPS (posterior sampling), MCG (manifold guidance), PGDM (pseudo-inverse guidance), and DDS (decoupled CG refinement). Recent benchmark (DM4CT, ICLR2026) suggests many diffusion-based CT methods (including more recent ones) achieve comparable reconstruction quality while differing substantially in computational cost. Motivated by this, our focus is introducing flow matching for sparse-view CT reconstruction and improving efficiency through velocity reuse, rather than incremental PSNR gains over every recent diffusion variant. We agree that adding more recent CT-specific baselines would further strengthen the evaluation and will clarify this limitation in updated version.
Perceptual metrics LPIPS(R2) We computed LPIPS and will include it in the revised version. Although ADMM-TV achieves slightly higher PSNR/SSIM than FMCT on AAPM 40-view reconstruction, its LPIPS is substantially worse (ADMM 0.272 vs FMCT 0.101/EFMCT 0.129), indicating weaker perceptual detail preservation.
Reuse strategy for diffusion/Poisson noise(R2) Due to the stochastic SDE nature of diffusion models, we empirically observe that score reuse is less stable for diffusion than for flow matching, often requiring more iterations and producing worse reconstructions. Under noisy measurements, DC corrections become less stable and interrupt reuse steps more frequently, although the strategy remains effective under moderate noise levels. We will include this in the discussion.
Training details and fairness(R2) The diffusion and flow models use identical architectures, datasets, optimizers, and training settings. The primary difference is the learning target: diffusion learns score, while flow matching learns the velocity field. We will add training details into the paper.
Velocity similarity drop near final steps(R2) We empirically observe that final sampling stages perform the most detailed refinement, leading to larger velocity deviations and lower cosine similarity. Accordingly, our initial implementation disables reuse in the final stages(flow_recon.py, line 88).
Geometry choice(R2) We use parallel-beam geometry to provide a controlled setting isolating reconstruction methodology from geometry-specific acquisition factors. Nevertheless, (E)FMCT remains geometry-agnostic. Preliminary fan-beam experiments show similar trends in reconstruction quality and acceleration.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
Reviewers are in principle in favor of this work but there are a number of concerns that need clarification. I agree with the work being of interest to the community in principle, as the efficiency of CT reconstruction is a major and important clinical concern. Please organize and rank the mentioned criticisms and address them in a rebuttal. A very important clarification is regarding the theory and the proof, which was mentioned by more than one reviewer. Another aspect that is crucial is to clarify if there are more recent state of the art works on CT reconstruction that were not discussed or compared to, and if so why these were omitted from the experimental setup.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
Majority of reviewers agree that this work is a good contribution for the MICCAI community. Concerns regarding the proof and the comparison to other methods have been convincingly addressed in the rebuttal. Minor remaining issues should be considered by the authors in case of acceptance. I agree with the majority assessment to accept this work.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
After carefully reviewing the rebuttal letter, I agree with Reviewer #3 that the authors have the potential to further improve the clarity and presentation of the manuscript. Nevertheless, I still find the work interesting and believe it contains sufficient novelty and practical value. Therefore, I lean toward accepting this paper.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper proposes EFMCT, an efficient flow matching framework for sparse-view CT reconstruction that reduces NFE by reusing velocity fields across adjacent sampling steps.
Reviewers broadly agree that the core contribution is novel, well-motivated, and practically meaningful. The most important contribution is achieving comparable quality with significantly fewer NFE, which is empirically well-supported.
The shared remaining concern is the proof. The rebuttal acknowledges a mathematical error, corrects the bound from O(M²Δt²) to O(M²Δt), and describes the fix verbally, with the authors promising to release the corrected proof in the public repository. R3 remains unconvinced without the corrected mathematics. However, since the core contribution lies in efficiency rather than the theoretical bound, and the empirical results directly demonstrate the efficiency gain, the proof issue is a presentation concern rather than a fundamental validity concern.
The strength outweighs the weaknesses and I recommend acceptance. That said, the authors should fix the proof in the final version to guarantee the correctness of the overall manuscript.