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Physics-Guided Flow Matching for CT Image Reconstruction

Davide Evangelista

arXiv:2608.28256v1cs.AIcs.CV

TL;DR

CT reconstruction is ill-posed, while diffusion-based priors can require costly, stochastic sampling. This work trains a high-resolution Rectified Flow Matching prior, evaluates it for sparse-view CT reconstruction, and reports consistent advantages over diffusion baselines, with numerical stabilization required for practical deployment.

  • Problem

    CT reconstruction from low-dose, sparse-view, or limited-angle measurements is ill-posed, and diffusion-prior methods face computational, scheduling, and stability limitations.

  • Method

    The paper trains a 256×256 chest-CT Rectified Flow Matching prior using two-stage augmentation and fine-tuning, then compares Flow Matching and diffusion-based reconstruction methods across sparse-view settings.

  • Results

    Flow Matching-based methods consistently outperform diffusion-based baselines across angular configurations; FlowDPS achieves the best overall PSNR, SSIM, and LPIPS performance.

  • Takeaways & Limitations

    Flow Matching provides a stable, efficient, and accurate alternative to diffusion priors for high-resolution and sparse-view CT reconstruction.

  • Takeaways & Limitations

    Practical reconstruction depends on corrections for normalized-to-physical image-domain mismatch, CT-operator amplification, and inexact discrete backprojection adjoints.

Abstract

from arXiv · show

Deep generative models have recently emerged as powerful priors for solving ill-posed inverse problems in CT, with diffusion-based approaches achieving state-of-the-art reconstruction performance. However, diffusion models typically rely on stochastic sampling procedures, long inference trajectories, and carefully tuned noise schedules, which can limit computational efficiency and numerical stability, especially at high spatial resolutions. In this work, we investigate Flow Matching as an alternative generative prior for CT reconstruction. We train a high-resolution Rectified Flow Matching model on 256x256 chest images from the Mayo Clinic Low-Dose CT dataset. To mitigate overfitting and limited anatomical variability, we employ a two-stage training strategy consisting of an initial phase with strong, anatomically informed data augmentation, followed by a fine-tuning phase with reduced or no augmentation to refine structural fidelity. The resulting model is capable of generating high-quality and anatomically coherent CT-like images, serving as a strong learned prior. We then evaluate multiple reconstruction methods specifically designed for Flow Matching models, including Plug-and-Play Flow, FlowDPS, Flower, and Flow-Priors (ICTM), and compare them against state-of-the-art diffusion-based reconstruction algorithms such as DDRM, DPS, and DiffPIR. Experimental results across several CT inverse problem settings show that Flow Matching-based approaches consistently outperform diffusion-based methods in terms of PSNR, SSIM, and perceptual quality, while requiring fewer sampling steps. Finally, we publicly release the trained Flow Matching model and accompanying code to facilitate reproducibility and future research. Overall, this work demonstrates that Flow Matching provides a stable, efficient, and effective alternative to diffusion models for high-resolution CT image reconstruction.

1 Introduction

CT reconstruction is ill-posed under incomplete or noisy acquisition, while diffusion priors improve quality at the cost of long stochastic sampling and careful scheduling. This work investigates Flow Matching as a high-resolution CT prior and evaluates it against diffusion-based reconstruction methods.

  • Motivation: Incomplete or noisy CT measurements can admit infinitely many reconstructions, requiring methods that preserve anatomical plausibility.The issue is especially pronounced in low-dose, sparse-view, and limited-angle settings.
  • Motivation: Diffusion priors improve CT reconstruction quality but typically require long sampling chains, noise scheduling, and stochastic solvers.These requirements increase computational cost and constrain inference flexibility, particularly for high-resolution medical imaging.
  • Proposed direction: Flow Matching deterministically transports samples from a simple base distribution to the data distribution by solving an ordinary differential equation.The formulation avoids explicit stochastic diffusion processes and supports higher-order numerical solvers.
  • Proposed direction: The study trains a high-resolution Rectified Flow Matching model on 256 × 256 Mayo Clinic Low-Dose CT chest images despite limited anatomical variability and overfitting risk.The dataset contains 3,306 acquisitions from 10 patients.
  • Contributions: A two-stage strategy combines strong augmentation with reduced- or no-augmentation fine-tuning to balance generalization and anatomical fidelity.The paper also releases trained weights and generation code for reproducibility.
  • Evaluation: Flow Matching reconstruction strategies are evaluated against diffusion baselines using PSNR, SSIM, and LPIPS under matched experimental settings.The evaluated Flow Matching methods include Plug-and-Play Flow, FlowDPS, FLOWER, and Flow-Priors (ICTM).

2 Related Work

Prior CT reconstruction methods include analytical, iterative, variational, and deep generative approaches, each involving trade-offs in artifacts, detail preservation, robustness, or tuning. Flow Matching has been less explored for inverse problems, and systematic high-resolution CT comparisons with diffusion methods remain limited.

  • Classical reconstruction: Filtered back-projection is fast under ideal sampling but produces severe artifacts in sparse-view, limited-angle, or noisy CT acquisition.Iterative methods address acquisition and noise modeling but require regularization for the ill-posed inverse problem.
  • Classical reconstruction: Variational methods using total variation or sparsity regularization reduce noise and artifacts but trade off structural detail and depend on parameter tuning.Their performance also depends on prior assumptions.
  • Deep learning: Early learning-based CT methods improve empirical reconstruction performance but can lack robustness to changes in acquisition geometry and noise levels.These approaches include FBP post-processing, model-based reconstruction, and end-to-end measurement-to-image mappings.
  • Generative priors: Diffusion models support approximate posterior sampling through iterative stochastic denoising and measurement-consistency updates.DDRM and DPS are examples of diffusion-based inverse-problem methods.
  • Generative priors: Flow Matching replaces stochastic diffusion with deterministic continuous-time dynamics that transport base-distribution samples to data samples through an ODE.Rectified Flow Matching further simplifies training while maintaining strong generative performance.
  • Research gap: Existing Flow Matching inverse-problem evaluations have focused mainly on low-resolution or non-medical datasets.A systematic high-resolution CT comparison with diffusion-based reconstruction remains largely unexplored.
  • Research gap: This work trains a Rectified Flow Matching prior on 256 × 256 CT images and compares multiple Flow Matching strategies with state-of-the-art diffusion methods.The comparison is designed to assess practical advantages and limitations in a clinically relevant setting.

3 Methodology

The methodology learns a Rectified Flow Matching prior from CT data and incorporates measurement consistency into continuous-time reconstruction dynamics. It uses two-stage augmentation and fine-tuning, then evaluates several Flow Matching reconstruction formulations.

  • 3.1 Inverse Problem Formulation: CT reconstruction is formulated as recovering an image x from linear measurements y = Kx + e, with Gaussian measurement noise and an ill-posed forward operator.The operator can represent sparse-view, limited-angle, or low-dose acquisition.
  • 3.1 Inverse Problem Formulation: The learned Flow Matching image distribution supplies the prior term in a Bayesian reconstruction framework.The prior models the complex distribution of medical images that is difficult to specify analytically.
  • 3.2 Flow Matching Prior: Flow Matching learns a time-dependent velocity field that transports samples from a base distribution to the CT image distribution through an ODE.A time-conditioned neural network approximates the true velocity field.
  • 3.2 Flow Matching Prior: Rectified Flow Matching defines an interpolation path between base and data samples and trains the network to reproduce its constant target velocity.The network parameters are learned by minimizing the Flow Matching loss.
  • 3.2 Flow Matching Prior: After training, deterministic generation numerically integrates the learned ODE from t = 0 to t = 1, using explicit Euler updates in this implementation.Higher-order solvers are identified as a future direction for improving low-step quality and stability.
  • 3.3 Training Strategy: Two-stage training first uses extensive augmentation, then reduced augmentation to retain diversity while refining anatomical fidelity.The second stage removes rotations and uses limited elastic deformation; 100 fine-tuning epochs use a learning rate of 5 · 10^-5.
  • 3.4 Flow Matching for CT Reconstruction: For inverse problems, the unknown image is treated as the flow’s initial condition and evolved under a velocity field modified by measurement consistency.PnP-Flow, FlowDPS, FLOWER, and ICTM balance learned prior dynamics with data-consistency forces derived from K.
  • 3.4 Flow Matching for CT Reconstruction: The reconstruction methods couple Flow Matching denoising estimates with likelihood-gradient, projection, or proximal data-consistency enforcement.FlowDPS applies a likelihood-gradient correction to the denoised estimate within each generative step.

4 Experimental Results

The experiments evaluate Flow Matching priors and reconstruction strategies for sparse-view CT under matched conditions, including practical adaptations for stable CT posterior sampling. Flow Matching achieves stronger generation and reconstruction quality than diffusion baselines, while the two-stage training strategy improves generation quality and anatomical coherence.

  • Practical considerations: CT posterior sampling requires mapping learned-prior iterates from [−1, 1] to the physical operator range [0, 1].This range conversion is applied whenever the projection operator computes residuals or data-consistency gradients.
  • Practical considerations: Large CT operator-induced gradients can cause numerical explosions, particularly early in sampling and under severe undersampling.The issue arises from the potentially large spectral norm of K^T K and the backprojected residual.
  • Unconditional generation: 10% to 20% KID decreases across step counts show that second-stage fine-tuning improves generation quality after strong augmentation.The fine-tuned model also exhibits improved anatomical coherence, while Flow Matching remains stronger than diffusion in low-step generation.
  • Quantitative reconstruction: Flow Matching methods consistently outperform diffusion baselines across angular settings, with FlowDPS reaching 36.64 dB PSNR, 0.9260 SSIM, and 0.1576 LPIPS.The reported LPIPS comparison at 60 angles is 0.2768 for DDRM versus 0.1759 for FlowDPS.
  • Qualitative reconstruction: Flow Matching reconstructions are sharper and preserve anatomical details better, while FlowDPS suppresses streaking without blur or noise amplification.Diffusion reconstructions recover global structure but lose fine details under severe angular sparsity; some extremely small symmetric bone structures remain unrecovered.

5 Discussion

The experiments identify numerical stabilization as essential for applying generative-prior posterior sampling to CT. Flow Matching priors outperform diffusion priors across angular configurations, with FlowDPS achieving the strongest overall results.

  • Stable CT reconstruction requires addressing normalized-to-physical range mismatch, CT-operator gradient amplification, and inexact backprojection.The adopted normalization, gradient scaling, clamping, gradient control, and CGLS-based corrections support stable convergence.
  • Flow Matching methods achieve higher PSNR and SSIM and lower LPIPS than diffusion-based baselines across all angular configurations.FlowDPS yields the best overall performance, while fine-tuning improves KID and anatomical fidelity in unconditional generation.

6 Conclusions

The paper develops and evaluates Rectified Flow Matching priors for high-resolution sparse-view CT reconstruction. A two-stage training strategy improves the learned prior, and Flow Matching methods outperform diffusion baselines while requiring numerical stabilization for robust convergence.

  • 6 Conclusions: Two-stage training combines strong anatomical augmentation with reduced or no augmentation during fine-tuning to improve fidelity and reduce distortions.Unconditional generation and KID evaluation provide a sanity-check for using the model as an inverse-problem prior.
  • 6 Conclusions: Flow Matching methods consistently outperform diffusion baselines across angular configurations, with FlowDPS best on PSNR, SSIM, and LPIPS.Qualitative results show improved preservation of fine anatomical structures and fewer artifacts in severely undersampled regimes.
  • 6 Conclusions: CT posterior sampling requires stabilization for domain mismatch, operator-induced amplification, and inexact backprojection.Normalization, gradient scaling, and CGLS-based corrections support convergence across methods and acquisition settings.
  • 6 Conclusions: Flow Matching is presented as a stable, efficient, and accurate alternative to diffusion models for high-resolution and sparse-view CT reconstruction.The paper identifies adaptive solvers, physics-based constraints, and extensions as future directions.

A Hyperparameter setting and grid search

The appendix explains how guidance scales differ across Flow Matching methods, how their updates enforce data consistency, and how hyperparameters are tuned for fair comparison.

  • Guidance-scale interpretation: Guidance scale νt balances data consistency against the generative prior, but its physical meaning differs across methods.FlowDPS and FLOWER generally use larger scales than PnP-Flow and ICTM because they inject consistency differently.
  • Method-specific updates: FlowDPS applies likelihood-gradient guidance within flow integration, whereas PnP-Flow and FLOWER use gradient-based correction steps.ICTM blends the Flow Matching estimate with a projected solution, with νt constrained to [0, 1].
  • Grid search: A validation grid search tunes each method’s νt separately for each angular configuration, selecting the value that maximizes PSNR.The number of time stamps is then chosen per method to balance reconstruction time and quality.
  • Final settings: The final Flow Matching settings use νt values of 5.0/1.0 for FlowDPS, 0.4/0.3 for PnP-Flow, 50/25 for FLOWER, and 0.9/0.8 for ICTM across 60/90 versus 120 angles.The methods use 500, 200, 300, and 100 steps, respectively.

B More experimental results

Additional experiments examine two representative test slices under 60, 90, and 120 projection angles. These case studies provide granular evidence about method behavior across anatomical features and noise realizations.

  • The analysis focuses on slices C081-45 and C081-79 reconstructed from 60, 90, and 120 projection angles.Individual cases complement metrics averaged over the full test dataset.
  • The individual-sample evaluation examines how methods handle specific anatomical features and varying noise realizations.

B.1 Sample-Specific Quantitative and Qualitative Analysis

Across two representative samples and 60, 90, and 120 projection angles, Flow Matching methods generally deliver stronger quantitative and visual reconstructions than diffusion baselines, especially under severe sparsity. FlowDPS is typically strongest in challenging settings, while diffusion methods become competitive as conditioning improves.

  • Quantitative analysis: Flow Matching methods consistently outperform diffusion baselines across sparsity levels, with particularly large gains in LPIPS.FlowDPS achieves the best overall performance on both samples in the most challenging sparse-view regime.
  • Qualitative analysis: Under severe sparsity, diffusion reconstructions preserve global anatomy but show oversmoothing, washed-out appearance, or blurred fine details.These issues are reported for DPS and DDRM in the zoomed regions of the visual comparisons.
  • Qualitative analysis: Flow Matching reconstructions produce sharper images, preserve small anatomical structures, and reduce visually salient artifacts in the sparse-view cases.The qualitative improvements are observed for both representative samples, including the more challenging C081-79 case.
  • Sample-specific comparison: Sample C081-79 is more difficult than C081-45, showing uniformly lower quantitative metrics and a reduced FlowDPS margin over other Flow Matching methods.FlowDPS remains the most robust method for this severely underdetermined regime.
  • Effect of acquisition geometry: At 120 projection angles, DDRM slightly surpasses FlowDPS in PSNR and SSIM on sample C081-79, although FlowDPS retains comparable visual quality with fewer perceptual artifacts.The differences remain small as the inverse problem becomes better conditioned.
  • Effect of acquisition geometry: All methods improve as projection angles increase, while diffusion methods become competitive mainly when the acquisition geometry is less ill-posed.The combined sample-level analysis supports the broader conclusions reported in the main manuscript.
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