# Functional Imaging Constrained Diffusion for Brain PET Synthesis from Structural MRI

arXiv: https://arxiv.org/abs/2405.02504 · HTML: https://mlsanity.com/paper/2405.02504/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 71 references that are in the map.
- First posted on arXiv 3 May 2024.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Generating Sentences from a Continuous Space](https://mlsanity.com/paper/1511.06349/) (2015)
- [MONAI: An open-source framework for deep learning in healthcare](https://mlsanity.com/paper/2211.02701/) (2022)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Diffusion-GAN: Training GANs with Diffusion](https://mlsanity.com/paper/2206.02262/) (2022)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [A review of domain adaptation without target labels](https://mlsanity.com/paper/1901.05335/) (2019)
- [Don't Blame the ELBO! A Linear VAE Perspective on Posterior Collapse](https://mlsanity.com/paper/1911.02469/) (2019)
- [Conversion Between CT and MRI Images Using Diffusion and Score-Matching Models](https://mlsanity.com/paper/2209.12104/) (2022)
- [Bidirectional Mapping Generative Adversarial Networks for Brain MR to PET Synthesis](https://mlsanity.com/paper/2008.03483/) (2020)
- [Unmasking Bias in Diffusion Model Training](https://mlsanity.com/paper/2310.08442/) (2023)
- [Synthesizing Multi-Tracer PET Images for Alzheimer's Disease Patients using a 3D Unified Anatomy-aware Cyclic Adversarial Network](https://mlsanity.com/paper/2107.05491/) (2021)
- [Gradient Domain Diffusion Models for Image Synthesis](https://mlsanity.com/paper/2309.01875/) (2023)

## Built on by (most cited first, 5 of 5)

- [CoCoLIT: ControlNet-Conditioned Latent Image Translation for MRI to Amyloid PET Synthesis](https://mlsanity.com/paper/2508.01292/) (2025)
- [RelA-Diffusion: Relativistic Adversarial Diffusion for Multi-Tracer PET Synthesis from Multi-Sequence MRI](https://mlsanity.com/paper/2602.21345/) (2026)
- [Adaptive Clinical-Aware Latent Diffusion for Multimodal Brain Image Generation and Missing Modality Imputation](https://mlsanity.com/paper/2603.09931/) (2026)
- [Translating MRI to PET through Conditional Diffusion Models with Enhanced Pathology Awareness](https://mlsanity.com/paper/2603.18896/) (2026)
- [Delta-Diffusion: Modeling Longitudinal Brain Amyloid-PET Trajectories via Conditional Poisson Diffusion Bridge](https://mlsanity.com/paper/2606.22216/) (2026)

## Abstract (arXiv)

Magnetic resonance imaging (MRI) and positron emission tomography (PET) are increasingly used in multimodal analysis of neurodegenerative disorders. While MRI is broadly utilized in clinical settings, PET is less accessible. Many studies have attempted to use deep generative models to synthesize PET from MRI scans. However, they often suffer from unstable training and inadequately preserve brain functional information conveyed by PET. To this end, we propose a functional imaging constrained diffusion (FICD) framework for 3D brain PET image synthesis with paired structural MRI as input condition, through a new constrained diffusion model (CDM). The FICD introduces noise to PET and then progressively removes it with CDM, ensuring high output fidelity throughout a stable training phase. The CDM learns to predict denoised PET with a functional imaging constraint introduced to ensure voxel-wise alignment between each denoised PET and its ground truth. Quantitative and qualitative analyses conducted on 293 subjects with paired T1-weighted MRI and 18F-fluorodeoxyglucose (FDG)-PET scans suggest that FICD achieves superior performance in generating FDG-PET data compared to state-of-the-art methods. We further validate the effectiveness of the proposed FICD on data from a total of 1,262 subjects through three downstream tasks, with experimental results suggesting its utility and generalizability.