# Delta-Diffusion: Modeling Longitudinal Brain Amyloid-PET Trajectories via Conditional Poisson Diffusion Bridge

arXiv: https://arxiv.org/abs/2606.22216 · HTML: https://mlsanity.com/paper/2606.22216/

## 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 29 references that are in the map.
- First posted on arXiv 20 Jun 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)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [Functional Imaging Constrained Diffusion for Brain PET Synthesis from Structural MRI](https://mlsanity.com/paper/2405.02504/) (2024)
- [Dual Meta-Learning with Longitudinally Generalized Regularization for One-Shot Brain Tissue Segmentation Across the Human Lifespan](https://mlsanity.com/paper/2308.06774/) (2023)
- [Diffusion Bridge Networks Simulate Clinical-grade PET from MRI for Dementia Diagnostics](https://mlsanity.com/paper/2510.15556/) (2025)
- [Identity Preserving Latent Diffusion for Brain Aging Modeling](https://mlsanity.com/paper/2503.09634/) (2025)
- [Hyperbolic Kernel Graph Neural Networks for Neurocognitive Decline Analysis from Multimodal Brain Imaging](https://mlsanity.com/paper/2507.02908/) (2025)
- [DuMeta++: Spatiotemporal Dual Meta-Learning for Generalizable Few-Shot Brain Tissue Segmentation Across Diverse Ages](https://mlsanity.com/paper/2602.07174/) (2026)
- [RelA-Diffusion: Relativistic Adversarial Diffusion for Multi-Tracer PET Synthesis from Multi-Sequence MRI](https://mlsanity.com/paper/2602.21345/) (2026)

## Abstract (arXiv)

While longitudinal brain PET imaging is the gold standard for quantifying the spatiotemporal accumulation of Beta-amyloid, its widespread clinical utility is constrained by high operational costs and cumulative radiation risks. Recent deep generative models show promise in longitudinal image synthesis; however, they often fail to capture subtle pathological progression due to identity drift and a persistent bias toward trivially replicating baseline signal intensities rather than modeling temporal transition. To this end, we propose Delta-Diffusion, a novel progression-aware framework that redefines longitudinal PET synthesis as a conditional Poisson Diffusion Bridge (PDB) process. Unlike standard diffusion models that start from Gaussian noise, our PDB formulation is mathematically anchored to the subject's baseline PET, effectively transforming the generative task into a conditional distribution transition of the amyloid trajectory. To handle heteroscedastic nature of PET imaging, we introduce a physically-grounded Poisson perturbation within a Diffusion Transformer (DiT). This architecture uses adaptive scale-shift modulation to precisely calibrate the synthesis with the elapsed clinical interval and structural MRI context. A volume-of-interest balanced objective is designed to emphasize sparse, high-risk regions of amyloid accumulation. Validated on two cohorts with 542 subjects, Delta-Diffusion demonstrates superior performance in capturing longitudinal variations in amyloid deposition compared to state-of-the-art methods, offering a robust computational framework for tracking disease progression.