# Manifold-Constrained PET Reconstruction with Learned Flow-Matching Priors

arXiv: https://arxiv.org/abs/2608.29158 · HTML: https://mlsanity.com/paper/2608.29158/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 14 of its 46 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 14 of 14)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Score-Based Generative Models for PET Image Reconstruction](https://mlsanity.com/paper/2308.14190/) (2023)
- [Likelihood-Scheduled Score-Based Generative Modeling for Fully 3D PET Image Reconstruction](https://mlsanity.com/paper/2412.04339/) (2024)
- [PET Image Reconstruction Using Deep Diffusion Image Prior](https://mlsanity.com/paper/2507.15078/) (2025)
- [Implicit neural representations for end-to-end PET reconstruction](https://mlsanity.com/paper/2503.21825/) (2025)

## Abstract (arXiv)

Image reconstruction for positron emission tomography (PET) is an ill-posed Poisson inverse problem that often suffers from severe noise amplification and artifacts. In this work, we introduce an unsupervised, optimization-based reconstruction framework that employs a flow-matching generative model as a learned manifold prior. We train the flow-matching model on high-quality PET images to learn a deterministic ordinary differential equation transport from a Gaussian latent distribution to the empirical PET image distribution, yielding a differentiable generator of anatomically plausible images. We incorporate this generator as an explicit manifold constraint into a regularized Poisson likelihood formulation. We solve the resulting optimization problem using an alternating direction method of multipliers algorithm, in which an expectation-maximization-type surrogate update enforces data consistency and a gradient-based latent-space projection enforces manifold proximity. We evaluate the proposed method on both simulated and real PET datasets, assessing dose-level robustness, lesion-insertion generalization, and cross-scanner transfer. Compared with conventional reconstruction methods and state-of-the-art deep learning baselines, the proposed method provides superior noise suppression, structural preservation, and quantitative accuracy, while maintaining high computational efficiency.