Unsupervised anomaly detection using Bayesian flow networks: application to brain FDG PET in the context of Alzheimer's disease

TL;DR

The paper tackles unsupervised anomaly detection in brain FDG-PET by reconstructing pseudo-healthy images to reveal disease-related abnormalities. It introduces AnoBFN, an extension of Bayesian flow networks that enables conditional generation under high spatially correlated noise and uses a recursive input-guided Bayesian update to preserve subject specificity. The authors present two main innovations: structured simplex noise with an accuracy schedule for conditional generation and a Bayesian update mechanism that fuses the input image during inference. On synthetic Alzheimer's disease–related hypometabolism in ADNI FDG-PET data, AnoBFN achieves state-of-the-art anomaly detection compared to beta-VAE, f-AnoGAN, and AnoDDPM, while providing sharper, subject-specific pseudo-healthy reconstructions and reduced false positives.

Abstract

Unsupervised anomaly detection (UAD) plays a crucial role in neuroimaging for identifying deviations from healthy subject data and thus facilitating the diagnosis of neurological disorders. In this work, we focus on Bayesian flow networks (BFNs), a novel class of generative models, which have not yet been applied to medical imaging or anomaly detection. BFNs combine the strength of diffusion frameworks and Bayesian inference. We introduce AnoBFN, an extension of BFNs for UAD, designed to: i) perform conditional image generation under high levels of spatially correlated noise, and ii) preserve subject specificity by incorporating a recursive feedback from the input image throughout the generative process. We evaluate AnoBFN on the challenging task of Alzheimer's disease-related anomaly detection in FDG PET images. Our approach outperforms other state-of-the-art methods based on VAEs (beta-VAE), GANs (f-AnoGAN), and diffusion models (AnoDDPM), demonstrating its effectiveness at detecting anomalies while reducing false positive rates.

Figures (3)

• Figure 1: Training and inference phases of the original Bayesian flow networks. Dashed lines correspond to samples from distributions, notations are defined in the main text.
• Figure 2: The white curves illustrate sample trajectories of $\mu$, the mean parameters of the latent variable $\bm{\theta}$, under both the schedule from graves_bayesian_2024 and our accuracy-based schedule. The background shows the probability flow distribution.
• Figure 3: Example of reconstructions and residual maps for a random subject in the test set. Top: synthetic abnormal scan, ground truth (real scan without anomalies) and pseudo-healthy reconstructions generated by the different models from the synthetic abnormal scan. Bottom row: mask used to simulate hypometabolism and difference maps computed between each reconstruction and the abnormal scan.