Unifying Reconstruction and Density Estimation via Invertible Contraction Mapping in One-Class Classification

Due to the difficulty in collecting all unexpected abnormal patterns, One-Class Classification (OCC) has become the most popular approach to anomaly detection (AD). Reconstruction-based AD method relies on the discrepancy between inputs and reconstructed results to identify unobserved anomalies. However, recent methods trained only on normal samples may generalize to certain abnormal inputs, leading to well-reconstructed anomalies and degraded performance. To address this, we constrain reconstructions to remain on the normal manifold using a novel AD framework based on contraction mapping. This mapping guarantees that any input converges to a fixed point through iterations of this mapping. Based on this property, training the contraction mapping using only normal data ensures that its fixed point lies within the normal manifold. As a result, abnormal inputs are iteratively transformed toward the normal manifold, increasing the reconstruction error. In addition, the inherent invertibility of contraction mapping enables flow-based density estimation, where a prior distribution learned from the previous reconstruction is used to estimate the input likelihood for anomaly detection, further improving the performance. Using both mechanisms, we propose a bidirectional structure with forward reconstruction and backward density estimation. Extensive experiments on tabular data, natural image, and industrial image data demonstrate the effectiveness of our method. The code is available at URD.