DDPM-PET: Diffusion Models in PET Imaging

• DDPM-PET is a generative framework that applies iterative denoising diffusion models to PET imaging, enabling enhanced attenuation correction and synthetic CT generation.
• It employs advanced conditioning strategies and diverse network architectures, such as U-Nets and transformer modules, to suppress artifacts and retain quantitative accuracy.
• Key applications include low-dose PET denoising, CT-free attenuation correction, and joint activity–attenuation estimation, demonstrating strong cross-center robustness.

Denoising Diffusion Probabilistic Models for PET (DDPM-PET) encompass a class of generative models leveraging the iterative denoising paradigm of diffusion models for Positron Emission Tomography (PET) image analysis, including attenuation correction, denoising, and synthetic data generation. These frameworks replace or augment traditional approaches such as CT-based attenuation correction, direct regression denoisers, or GAN-based methods, offering improved fidelity, artifact suppression, and uncertainty quantification. Recent works have established DDPM-PET as a competitive or superior alternative to conventional protocols across a range of PET imaging tasks, notably including CT synthesis from PET, attenuation and scatter correction, robust low-dose PET restoration, and realistic synthetic paired PET–CT data generation.

1. Mathematical Foundation and Conditioning Strategies

DDPM-PET models are built upon the standard denoising diffusion probabilistic model (DDPM) principle, where a target image $x_0$ (e.g., PET or CT volume) is incrementally corrupted by Gaussian noise in the forward process: $$q(x_t \mid x_{t-1}) = \mathcal{N}(x_t; \sqrt{1-\beta_t} x_{t-1}, \beta_t I)$$ implemented with a predefined schedule $\{ \beta_t \}_{t=1}^T$ (e.g., cosine, linear). The reverse generative process is modeled as a parameterized Gaussian: $$p_\theta(x_{t-1} \mid x_t, c) = \mathcal{N}(x_{t-1}; \mu_\theta(x_t, t, c), \Sigma_t I)$$ where $c$ denotes conditioning variables—these can include uncorrected PET, early-phase PET, anatomical priors, or auxiliary metadata. The network learns to estimate the additive noise $\epsilon_\theta(x_t, t, c)$, with the conditional mean: $$\mu_\theta(x_t, t, c) = \frac{1}{\sqrt{1-\beta_t}} \left( x_t - \frac{\beta_t}{\sqrt{1-\bar\alpha_t}} \epsilon_\theta(x_t, t, c) \right)$$ and is trained via an expected mean squared error between true and predicted noise: $$L_{\rm simple} = \mathbb{E}_{x_0, t, \epsilon} \left[ \| \epsilon - \epsilon_\theta(x_t, t, c) \|^2 \right]$$ Conditioning strategies are diverse:

• PET-to-CT synthesis and attenuation correction: Conditional on non-attenuation-corrected PET, often using multiview ensemble or auxiliary encoders (St-Georges et al., 28 Oct 2025).
• Joint activity–attenuation: Directly modeling $(\lambda, \mu)$ and leveraging joint priors for PET activity and attenuation estimation, essential for crosstalk mitigation in non-TOF PET (Phung-Ngoc et al., 2024).
• Auxiliary information: Incorporation of temporal/dose embeddings, anatomical priors (e.g., MRI/CT), or metadata-guided conditioning (text prompts, ControlNet) (Yu et al., 28 Feb 2025, Yu et al., 2024).
• Hybrid representation: Some frameworks perform coarse-to-fine prediction, where deterministic modules produce initial estimates refined by diffusion (Han et al., 2023).

2. Network Architectures and Model Variants

Typical DDPM-PET implementations employ U-Net backbones with residual and attention modules, but recent research has diversified model architectures:

• 2D and 3D U-Net variants: Slice-wise DDPMs for PET-to-CT synthesis (St-Georges et al., 28 Oct 2025), and fully 3D U-Nets for dose-aware denoising (Xie et al., 2024, Jing et al., 2 Mar 2026), sometimes leveraging slab-based 2.5D approaches for computational tractability (Cho et al., 13 Nov 2025).
• Multiview and ensemble methods: Independent DDPMs are trained per orthogonal plane (axial/coronal/sagittal), with inference fusion via majority or closeness voting to suppress artifacts and enhance 3D consistency (St-Georges et al., 28 Oct 2025).
• Hybrid modules: Alternation of CNN blocks (for local context) and pixel-wise Transformer blocks (for global context) enables robust prediction in low-SNR regimes (Hong et al., 2024).
• Paired and linked DDPMs: Multimodal generation of paired PET–CT–segmentation maps is achieved by running synchronized DDPMs for each modality, exchanging cross-modal conditional features at every denoising step (Bradbury et al., 2024).
• Attention and cross-attention mechanisms: Semantic guidance via text-prompted embeddings (CLIP) with cross-attention integration for PET denoising (Yu et al., 28 Feb 2025).
• ControlNet and plug-and-play modules: Post-hoc adaptivity using ControlNet branches to update only the conditional path during transfer to new scanners or dose protocols (Yu et al., 2024).
• Consistency models: Highly efficient, transformer-based architectures that distill the denoising process to two or three direct "consistency" steps, reducing inference latency by an order of magnitude while maintaining high quantitative accuracy (Pan et al., 2023).

3. Core PET Imaging Applications

The DDPM-PET paradigm has been applied across a spectrum of PET imaging tasks:

• CT-free attenuation correction: High-resolution pseudo-CT synthesis from non-attenuation-corrected PET, enabling attenuation correction without additional CT/MRI acquisitions (St-Georges et al., 28 Oct 2025, Cho et al., 13 Nov 2025). The generative approach preserves PET anatomical detail, avoids misregistration, and eliminates extra dose.
• Direct attenuation and scatter correction: Synthesis of ASC PET from non-attenuation and non-scatter corrected PET using generation-prior DDPM, substantially reducing sampling time (GPDM) (Cho et al., 13 Nov 2025).
• Low-dose PET denoising: Dose-aware 3D DDPMs trained across a wide dose spectrum achieve superior NRMSE, PSNR, and lesion quantification over U-Net and GAN baselines; strong cross-center generalizability and clinically validated image quality (Xie et al., 2024).
• Dual-time/delayed scan prediction: Diffusion models with spatial-temporal conditioning learn the tracer uptake evolution, outperforming standard DDPMs, GANs, and transformers in delayed PET synthesis (Hong et al., 2024).
• Sinogram-to-image PET reconstruction: Posterior-mean DDPMs implement explicit perception-distortion tradeoff for robust, artifact-free image generation from sinogram data, providing clear separation of distortion and perceptual quality (Sun et al., 11 Mar 2025).
• Paired data synthesis and augmentation: Multi-DDPM frameworks support joint PET, CT, and tumor-segmentation synthesis for data augmentation, accelerating convergence in downstream clinical tasks and enabling data-scarce segmentation (Bradbury et al., 2024).
• Joint activity–attenuation estimation: DPS-based DDPMs address activity–attenuation crosstalk, outperforming MLAA and conventional joint reconstructions in non-TOF and simulated TOF settings (Phung-Ngoc et al., 2024).
• Pseudo-anatomy guidance: PET–to–MRI conditional diffusion enables anatomically guided MAP PET reconstruction even when MRI is unavailable (Gan et al., 2024).

4. Quantitative Evaluation and Comparative Analysis

DDPM-PET frameworks report comprehensive quantitative and qualitative evaluations:

• Accuracy metrics: MAE, RMSE, PSNR, SSIM, NRMSE, and region-of-interest (ROI) error relative to CT or PET references. For pseudo-CT synthesis, MAE ≈ 32 HU and PET ROI error ≈ 1.5% are typical (St-Georges et al., 28 Oct 2025).
• Lesion-level and regional quantification: Lesion SUV bias, contrast recovery, and Dice scores using segmentation networks or Monte Carlo lesion studies, with SUV bias <3% across organ/uptake levels (Xie et al., 2024).
• Clinical reader validation: Board-certified nuclear medicine physicians rated DDPM-PET reconstructions at least as good as, or superior to, full-dose reference images (Xie et al., 2024).
• Computational efficiency: Voting ensemble methods and generation-prior initialization reduce inference time (200 vs. 1000 steps) (Cho et al., 13 Nov 2025), while PET consistency models (PET-CM) reduce full patient inference by up to 12x (Pan et al., 2023).
• Comparison with baselines: Across datasets, DDPM-PET models consistently exceed U-Net, GAN, and VAE-based methods in PSNR (by ≈1–5 dB), SSIM (by ≈0.01–0.03), and NMAE (by 0.01–0.05), with state-of-the-art performance on both internal and external evaluation sets (Xie et al., 2024, Jing et al., 2 Mar 2026, Cho et al., 13 Nov 2025).

Task	Metric	Typical DDPM-PET Value	Competing Methods
Pseudo-CT (HU MAE)	MAE	32 ± 10.4	GAN/TFM: 38–45
PET denoising (SSIM)	SSIM	0.95–0.997	U-Net: 0.94; GAN: 0.93
Dose-aware (RMSE/NRMSE)	NRMSE	0.24–0.30	DDIM: >0.34
Synthesis speed (per vol.)	Time (min)	15 (DDPM), 1 (PET-CM)	GAN: <1; vanilla DDPM: 360
Lesion bias (SUV)	% Bias	<3%	DDIM: >10%

Details for table entries: (St-Georges et al., 28 Oct 2025, Xie et al., 2024, Pan et al., 2023, Cho et al., 13 Nov 2025, Jing et al., 2 Mar 2026)

5. Strengths, Limitations, and Future Directions

Key strengths of DDPM-PET methodologies:

• Artifact suppression: Avoidance of GAN mode collapse and blurring; preservation of anatomical detail.
• Robustness to input variations: Dose-aware and multi-institutional generalizability enables deployment across centers, scanners, and dose levels.
• Modularity and adaptability: ControlNet and plug-and-play branches allow rapid adaptation to new protocols without backbone retraining (Yu et al., 2024).
• Consistent uncertainty quantification: Posterior sampling and ensemble outputs.
• Support for multimodality and data fusion: Joint or conditional modeling with CT/MRI/segmentation data.

Limitations include:

• Computational burden: Full 3D DDPMs or per-slice inference is resource-intensive, though advances like consistency models mitigate this.
• Memory tradeoffs: 2.5D methods trade global spatial context for tractability.
• Uncertainty in ultra-low-dose and out-of-distribution: Further work is needed for scenarios beyond FDG, such as pediatric, rare tracers, and protocol drift.
• Full 3D and multi-modal extension: Routine multi-tracer, multi-modal, and end-to-end PET/CT/MR fusion applications remain open for improvement.

Future research is aimed at integrating more efficient sampling (e.g., DDIM, DPM-Solver), improving out-of-distribution generalization, and enabling continuous-time and variable noise schedules (Cho et al., 13 Nov 2025, Jing et al., 2 Mar 2026). Additionally, integration with clinical workflow and regulatory compliance for CT-free attenuation correction are anticipated translational milestones.

6. Summary and Outlook

DDPM-PET techniques leverage conditional denoising diffusion models to resolve longstanding challenges in PET image processing, including CT-less attenuation correction, low-dose denoising, artifact reduction, and synthetic dataset augmentation. They achieve or surpass state-of-the-art performance, with strong quantitative accuracy, artifact suppression, and cross-protocol robustness, and provide paths for uncertainty quantification and plug-and-play conditioning. With ongoing advances in network efficiency, conditional representation, and clinical validation, DDPM-PET frameworks are poised to redefine quantitative and qualitative standards in PET imaging and reconstruction (St-Georges et al., 28 Oct 2025, Cho et al., 13 Nov 2025, Xie et al., 2024, Pan et al., 2023, Phung-Ngoc et al., 2024).