Temporal Knowledge Graph (TKG) extrapolation aims to predict future facts from observed historical events. Existing methods usually achieve this goal by jointly modeling local historical evolution and long-range historical contexts. First, local evolution modeling often summarizes local history into an overall evolving representation, where query-relevant local deviations may not be sufficiently exploited as useful predictive features. Second, existing long-range history modeling often treats historical recurrence as a stable cue, while overlooking that its reliability may vary across relations and recent contexts. To address these issues, we propose DyHist, a query-aware historical dynamics modeling framework for TKG extrapolation. DyHist captures local dynamics by separating recent evidence from medium-range context and explicitly modeling their query-relevant deviations as predictive features. It further uses a relation-aware historical prior to calibrate candidate scores with time-decayed support, recent trends, and relation-specific strength, enabling recurrence signals to contribute differently across relations and recent contexts. Experiments on four benchmarks show that DyHist achieves the best MRR against recent baselines. Code is available at https://github.com/PANPANKK/DyHist.

Temporal Knowledge Graph (TKG) extrapolation seeks to infer future facts from time-varying relational histories. Recent diffusion-based approaches improve uncertainty modeling through generative denoising, but their aggregated conditioning on subject histories may insufficiently distinguish query-specific evidence from non-salient historical facts, thereby diluting target-discriminative signals. To bridge this gap, we propose **FreqDiff**, a **Freq**uency-aware **Diff**usion framework for TKG extrapolation. Specifically, FreqDiff formulates future object prediction as query-slot denoising and develops a dual-stream denoiser that integrates temporal dependency modeling with context-aware spectral calibration. The spectral branch synthesizes history-conditioned filters from learnable bases to adaptively re-calibrate denoising representations, while a frequency-domain regularizer is proposed to align the denoised target with the gold object in spectral space. Experiments on four public TKG benchmarks demonstrate that FreqDiff achieves state-of-the-art performance.