Streaming Anomaly Detection in Contaminated Manifold-Structured High-Dimensional Data

High-dimensional observations, such as material spectra and industrial process measurements, often concentrate near low-dimensional manifolds and arrive as streams during continuous scanning and process monitoring. Detecting anomalies in these streams requires learning emerging normal patterns without absorbing sparse anomalies into the background. Both emerging normal patterns and anomalies can receive high anomaly scores from a model trained on earlier observations, so its scores alone cannot determine which samples should guide subsequent learning. We propose Evolving Score Fields (ESF), a streaming anomaly detection framework for manifold-structured observations. By learning gradients of the log density, its score model implicitly represents the background distribution and its local geometry. ESF distinguishes compatibility with the learned background from support within the current block. Score-direction consistency measures departure from the learned field, while neighborhood support allows well-supported new patterns to enter adaptation even when the existing field assigns them high anomaly scores. Selected samples update the field through local denoising score matching with LoRA adapters and historical replay. The adapted field scores the current block, and a sample-aware merge carries the update into subsequent blocks. This connects anomaly detection and background learning within one evolving field, without anomaly labels or full-model retraining. Experiments on HyperAD and sparse-fault TEP streams demonstrate ESF's strong detection performance across spectral and industrial data.