RelA-Diffusion: Relativistic Adversarial Diffusion for Multi-Tracer PET Synthesis from Multi-Sequence MRI

Minhui Yu; Yongheng Sun; David S. Lalush; Jason P Mihalik; Pew-Thian Yap; Mingxia Liu

eess.IVFeb 24, 2026

RelA-Diffusion: Relativistic Adversarial Diffusion for Multi-Tracer PET Synthesis from Multi-Sequence MRI

Authors: Minhui Yu, Yongheng Sun, David S. Lalush, Jason P Mihalik, Pew-Thian Yap, Mingxia Liu

Organizations: Department of Radiology and Biomedical Research Imaging Center (BRIC), University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA. · Joint Department of Biomedical Engineering, University of North Carolina at Chapel Hill and North Carolina State University, Chapel Hill, NC 27599, USA. · Department of Exercise and Sport Science, UNC-CH, Chapel Hill, NC 27599, USA.

Abstract

Multi-tracer positron emission tomography (PET) provides critical insights into diverse neuropathological processes such as tau accumulation, neuroinflammation, and $β$ -amyloid deposition in the brain, making it indispensable for comprehensive neurological assessment. However, routine acquisition of multi-tracer PET is limited by high costs, radiation exposure, and restricted tracer availability. Recent efforts have explored deep learning approaches for synthesizing PET images from structural MRI. While some methods rely solely on T1-weighted MRI, others incorporate additional sequences such as T2-FLAIR to improve pathological sensitivity. However, existing methods often struggle to capture fine-grained anatomical and pathological details, resulting in artifacts and unrealistic outputs. To this end, we propose RelA-Diffusion, a Relativistic Adversarial Diffusion framework for multi-tracer PET synthesis from multi-sequence MRI. By leveraging both T1-weighted and T2-FLAIR scans as complementary inputs, RelA-Diffusion captures richer structural information to guide image generation. To improve synthesis fidelity, we introduce a gradient-penalized relativistic adversarial loss to the intermediate clean predictions of the diffusion model. This loss compares real and generated images in a relative manner, encouraging the synthesis of more realistic local structures. Both the relativistic formulation and the gradient penalty contribute to stabilizing the training, while adversarial feedback at each diffusion timestep enables consistent refinement throughout the generation process. Extensive experiments on two datasets demonstrate that RelA-Diffusion outperforms existing methods in both visual fidelity and quantitative metrics, highlighting its potential for accurate synthesis of multi-tracer PET.

Figures & tables

Fig. 1: Illustration of the proposed relativistic adversarial diffusion (RelA-Diffusion) framework that synthesizes multi-tracer PET images from multi-sequence MRI input such as T1-weighted (T1w) and T2-FLAIR (T2F) MRIs.

x_{t-1}=\frac{1}{\sqrt{\alpha_{t}}}\left(x_{t}-\frac{1-\alpha_{t}}{\sqrt{1-\bar{\alpha}_{t}}}\hat{\epsilon}\right)+\sigma_{t}z

Algorithm 2 Inference with Trained RelA-Diffusion Generator

Method

Synthesized TAU-PET Image

Synthesized PBR-PET Image

Synthesized PIB-PET Image

PSNR

\uparrow

SSIM

\uparrow

MAE

\downarrow

Sig.

PSNR

\uparrow

SSIM

\uparrow

MAE

\downarrow

Sig.

PSNR

\uparrow

SSIM

\uparrow

MAE

\downarrow

Sig.

CycleGAN [ 10 ]

27.506

\pm

1.598

0.869

\pm

0.013

0.017

\pm

0.004

*

28.065

\pm

2.687

0.833

\pm

0.022

0.017

\pm

0.007

*

24.954

\pm

2.274

0.846

\pm

0.017

0.024

\pm

0.010

*

DDGAN [ 16 ]

25.448

\pm

2.373

0.892

\pm

0.015

0.025

\pm

0.009

*

25.201

\pm

3.044

0.884

\pm

0.017

0.027

\pm

0.011

*

26.382

\pm

2.561

0.870

\pm

0.018

0.021

\pm

0.010

*

StableDiff [ 26 ]

26.483

\pm

4.426

0.881

\pm

0.031

0.023

\pm

0.015

*

28.845

\pm

2.681

0.892

\pm

0.019

0.015

\pm

0.006

*

25.245

\pm

1.735

0.852

\pm

0.013

0.023

\pm

0.007

*

NFlow [ 27 ]

27.615

\pm

3.490

0.881

\pm

0.020

0.019

\pm

0.010

*

28.844

\pm

2.030

0.887

\pm

0.013

0.015

\pm

0.004

*

24.522

\pm

1.304

0.805

\pm

0.017

0.024

\pm

0.004

*

DiffGAN [ 17 ]

24.980

\pm

2.330

0.884

\pm

0.013

0.026

\pm

0.009

*

23.112

\pm

2.938

0.870

\pm

0.021

0.034

\pm

0.012

*

23.491

\pm

2.640

0.855

\pm

0.021

0.031

\pm

0.013

*

TABLE I: Quantitative results of eight methods for TAU-, PBR- and PIB-PET generation on NFL-LONG (best results in bold). The column Sig. indicates statistically significant (

p<0.05

) via

t

-test on SSIM.

Fig. 3: Visualization of test ADNI TAU-PET images synthesized by 8 methods, and difference (Diff) maps. The ground-truth (GT) PET images along with the input T1w and T2F MRIs are displayed at the bottom with the corresponding subject IDs.

Fig. 4: Region-level quantitative evaluation on NFL-LONG. (a) Scatter plots of predicted vs. ground-truth volume-of-interest (VOI) mean SUVr for TAU-PET across eight methods and five tau-related VOIs (Frontal, Mesial Temporal, Meta Temporal, Temporo-Parietal, and Universal) [ 30 ] , with MAE and RMSE reported in each panel. (b) Comparison of SSIM results across the same five VOIs [ 30 ] .

Method	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$
CycleGAN [ 10 ]	23.766 $\pm$ 3.170	0.843 $\pm$ 0.034	0.030 $\pm$ 0.015
DDGAN [ 16 ]	20.563 $\pm$ 3.126	0.839 $\pm$ 0.028	0.045 $\pm$ 0.018
StableDiff [ 26 ]	22.179 $\pm$ 3.279	0.838 $\pm$ 0.035	0.038 $\pm$ 0.018
NFlow [ 27 ]	25.449 $\pm$ 2.635	0.851 $\pm$ 0.033	0.024 $\pm$ 0.010
DiffGAN [ 17 ]	24.797 $\pm$ 2.887	0.862 $\pm$ 0.029	0.026 $\pm$ 0.011
FICD [ 13 ]	18.624 $\pm$ 2.934	0.831 $\pm$ 0.028	0.058 $\pm$ 0.021

TABLE II: Quantitative results of eight methods for synthesized ADNI TAU-PET images (best results in bold).

Method	Synthesized TAU-PET Image			Synthesized PBR-PET Image			Synthesized PIB-PET Image
Method	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$
w/oRA	28.156 $\pm$ 4.304	0.908 $\pm$ 0.023	0.019 $\pm$ 0.012	29.311 $\pm$ 2.547	0.912 $\pm$ 0.018	0.015 $\pm$ 0.006	25.408 $\pm$ 2.182	0.877 $\pm$ 0.010	0.022 $\pm$ 0.006
w/oGP	18.401 $\pm$ 2.780	0.780 $\pm$ 0.027	0.061 $\pm$ 0.021	20.947 $\pm$ 2.732	0.786 $\pm$ 0.029	0.045 $\pm$ 0.013	16.855 $\pm$ 0.953	0.764 $\pm$ 0.008	0.066 $\pm$ 0.007
w/oRAGP	24.956 $\pm$ 4.644	0.877 $\pm$ 0.038	0.029 $\pm$ 0.016	29.261 $\pm$ 4.173	0.900 $\pm$ 0.029	0.016 $\pm$ 0.010	23.721 $\pm$ 3.166	0.850 $\pm$ 0.020	0.029 $\pm$ 0.010
w/oT2F	28.109 $\pm$ 4.457	0.898 $\pm$ 0.029	0.019 $\pm$ 0.013	29.490 $\pm$ 2.380	0.905 $\pm$ 0.017	0.014 $\pm$ 0.005	25.366 $\pm$ 1.814	0.863 $\pm$ 0.012	0.022 $\pm$ 0.005
w/oT1w	26.022 $\pm$ 4.721	0.887 $\pm$ 0.035	0.026 $\pm$ 0.016	29.894 $\pm$ 2.839	0.907 $\pm$ 0.020	0.014 $\pm$ 0.006	23.695 $\pm$ 2.748	0.851 $\pm$ 0.014	0.029 $\pm$ 0.008

TABLE III: Quantitative results achieved by RelA-Diffusion, as well as their degraded variants for multi-tracer PET generation on NFL-LONG, with best results shown in bold.

Method	Synthesized TAU-PET Image			Synthesized PBR-PET Image			Synthesized PIB-PET Image			Inference Time $\downarrow$
Method	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	MAE $\downarrow$	Inference Time $\downarrow$
RelA-Diffusion	28.314 $\pm$ 3.392	0.898 $\pm$ 0.017	0.017 $\pm$ 0.009	29.324 $\pm$ 2.437	0.898 $\pm$ 0.017	0.015 $\pm$ 0.006	26.270 $\pm$ 1.687	0.861 $\pm$ 0.012	0.020 $\pm$ 0.006	126.778
RelA-Diffusion-Latent	27.921 $\pm$ 3.902	0.900 $\pm$ 0.022	0.019 $\pm$ 0.011	28.823 $\pm$ 1.395	0.901 $\pm$ 0.012	0.015 $\pm$ 0.004	24.523 $\pm$ 2.076	0.865 $\pm$ 0.010	0.024 $\pm$ 0.005	0.778

TABLE IV: Quantitative results and inference time of RelA-Diffusion and RelA-Diffusion-Latent for TAU-, PBR-, and PIB-PET generation on NFL-LONG. Inference time is measured in seconds per 3D volume.

Fig. 5: Downstream regression performance for age, MMSE, and MoCA prediction using synthesized PET (syn-PET) generated from ADNI TAU images together with MRI, in comparison with MRI-only inputs.

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