Flow+Diff: Unifying Flow and Diffusion Representations for Multivariate Time Series Anomaly Detection

Many existing multivariate time series anomaly detection methods formulate anomaly detection as a reconstruction problem, where detections are derived from reconstruction errors in the time domain. While effective for large deviations, reconstruction-based scoring struggles with subtle anomalies where only a small subset of features deviates slightly. In such cases, most features are well reconstructed, causing the overall reconstruction error to remain low and indistinguishable from normal data. To address these challenges, we propose Flow+Diff, a novel framework that detects anomalies via discrepancies in a latent space, where two complementary representations, induced by distinct modeling paradigms, diverge under anomalous inputs. One representation is obtained via a normalizing flow, which provides an invertible mapping that preserves temporal dependencies and captures inter-feature dependencies. The other is produced by a diffusion model that learns the distribution of normal samples in the latent space via a stochastic denoising process. When given anomalous inputs, the normalizing flow maps the inputs to latent representations that lie in low-probability regions of the learned latent distribution, while the diffusion model generates representations aligned with normal data distributions, resulting in a pronounced discrepancy between the two. We compute the anomaly score based on this latent-space discrepancy, thereby shifting anomaly detection from the time domain to the latent space. Finally, the invertibility of the normalizing flow enables reconstruction in the time domain, facilitating interpretation of anomalous features. Extensive experiments across six benchmark datasets show that Flow+Diff achieves state-of-the-art performance on four datasets against competitive baselines.