# Unsupervised Brain Anomaly Detection as a Bayesian Inverse Problem with Diffusion Prior

arXiv: https://arxiv.org/abs/2609.24265 · HTML: https://mlsanity.com/paper/2609.24265/

## 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 25 references that are in the map.
- First posted on arXiv 21 Sep 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)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Diffusion Models for Medical Anomaly Detection](https://mlsanity.com/paper/2203.04306/) (2022)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Mask, Stitch, and Re-Sample: Enhancing Robustness and Generalizability in Anomaly Detection through Automatic Diffusion Models](https://mlsanity.com/paper/2305.19643/) (2023)
- [Patched Diffusion Models for Unsupervised Anomaly Detection in Brain MRI](https://mlsanity.com/paper/2303.03758/) (2023)
- [Diffusion Models with Implicit Guidance for Medical Anomaly Detection](https://mlsanity.com/paper/2403.08464/) (2024)
- [Evaluation of pseudo-healthy image reconstruction for anomaly detection with deep generative models: Application to brain FDG PET](https://mlsanity.com/paper/2401.16363/) (2024)
- [MAD-AD: Masked Diffusion for Unsupervised Brain Anomaly Detection](https://mlsanity.com/paper/2502.16943/) (2025)
- [IterMask2: Iterative Unsupervised Anomaly Segmentation via Spatial and Frequency Masking for Brain Lesions in MRI](https://mlsanity.com/paper/2406.02422/) (2024)
- [Binary Noise for Binary Tasks: Masked Bernoulli Diffusion for Unsupervised Anomaly Detection](https://mlsanity.com/paper/2403.11667/) (2024)
- [Unsupervised anomaly detection using Bayesian flow networks: application to brain FDG PET in the context of Alzheimer's disease](https://mlsanity.com/paper/2507.17486/) (2025)

## Abstract (arXiv)

Unsupervised anomaly detection (UAD) aims to localize abnormal regions in medical scans without pixel-level annotations. A typical strategy seeks to reconstruct a pseudo-healthy image that preserves subject-specific anatomy. Recently, diffusion models have been proposed to perform UAD. However, these methods rely on heuristic noise schedules or synthetic corruptions to balance subject-specificity and anomaly removal. In this work, we propose an alternative formulation of UAD as a Bayesian inverse problem under a diffusion prior. First, we introduce a latent spatial anomaly mask that models pixel-wise consistency between a test image and its latent corresponding pseudo-healthy image. Then, we propose an approximation of the unknown generation process that links healthy anatomy, anomalies, and the observed image, enabling a well-defined likelihood within the Bayesian framework. Building on recent advances in diffusion-based inverse problem methods, we jointly infer the pseudo-healthy image and the anomaly mask via annealed posterior sampling. We evaluate our approach on FDG PET (ADNI) and FLAIR MRI (BraTS 2021), demonstrating improved anomaly localization performance compared to other diffusion-based approaches and validating the contribution of our introduced model. Our code is available at https://github.com/HuguesRoy/UAD_DAPS.