Where Can Normality Go: Learning Admissible Futures for Time Series Anomaly Detection

Time-series anomaly detection commonly uses prediction errors or likelihood-based scores to identify deviations from normal temporal evolution. However, even under the same observed history, normal evolution can follow multiple future trajectories, so deviation from a single expected trajectory need not indicate an anomaly. The set of normal continuations also varies with history: the same future trajectory may be admissible after one historical state but inconsistent with another. This motivates representing temporal normality as a history-conditioned region of admissible future trajectories and detecting anomalies when an observed future falls outside it. Learning such a region is challenging because each training history reveals only one realized normal continuation, providing a sample within the region without directly revealing its boundary. To address this, we propose **FutureBound**, a framework that learns this boundary implicitly through local future-space exploration and selective adversarial optimization. A context-conditioned generator produces multiple locally anchored yet diverse trajectories as probes around observed normal continuations. A discriminator then learns context-future compatibility by contrasting the observed continuation with nearby probes under the same history. To refine this distinction, the generator is adversarially optimized to make selected probes increasingly challenging to the discriminator, with proximity-based and direction-aware selection concentrating these updates around normal evolution. This interaction learns an implicit, potentially asymmetric boundary without prescribing its geometry in advance. At inference time, the learned compatibility directly measures whether an observed future agrees with its preceding history. Extensive experiments on four real-world time-series benchmarks demonstrate consistent improvements over existing methods, supporting history-conditioned future admissibility as a flexible reference for distinguishing anomalous deviations from normal temporal variation.