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

2026-06-20

AI Summary

This study addresses the high cost and radiation risk of longitudinal brain PET imaging, as well as the inability of existing deep generative models to accurately capture the subtle pathological progression of β-amyloid, which often leads to identity drift or mere replication of baseline scans. To overcome these limitations, the authors propose a conditional Poisson diffusion bridge framework that leverages a subject’s baseline PET as an anchor while integrating structural MRI and clinical time intervals to precisely simulate the spatiotemporal evolution of amyloid deposition. The method incorporates physics-informed Poisson perturbations, an adaptive scaling modulation mechanism, and a lesion-aware balanced loss to effectively model heteroscedasticity and sparse, high-risk regions. Evaluated on two cohorts comprising 542 subjects using a diffusion Transformer architecture, the approach significantly outperforms current methods in faithfully reconstructing longitudinal dynamics.

Abstract

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.

Problem

• longitudinal PET synthesis
• amyloid progression
• identity drift
• temporal transition
• pathological trajectory

Innovation

• Conditional Poisson Diffusion Bridge
• Longitudinal PET Synthesis
• Diffusion Transformer
• Amyloid Trajectory Modeling
• Heteroscedastic Image Generation