  Reconstruction-based methods have been commonly used for unsupervised anomaly
detection, in which a normal image is reconstructed and compared with the given
test image to detect and locate anomalies. Recently, diffusion models have
shown promising applications for anomaly detection due to their powerful
generative ability. However, these models lack strict mathematical support for
normal image reconstruction and unexpectedly suffer from low reconstruction
quality. To address these issues, this paper proposes a novel and
highly-interpretable method named Masked Diffusion Posterior Sampling (MDPS).
In MDPS, the problem of normal image reconstruction is mathematically modeled
as multiple diffusion posterior sampling for normal images based on the devised
masked noisy observation model and the diffusion-based normal image prior under
Bayesian framework. Using a metric designed from pixel-level and
perceptual-level perspectives, MDPS can effectively compute the difference map
between each normal posterior sample and the given test image. Anomaly scores
are obtained by averaging all difference maps for multiple posterior samples.
Exhaustive experiments on MVTec and BTAD datasets demonstrate that MDPS can
achieve state-of-the-art performance in normal image reconstruction quality as
well as anomaly detection and localization.
