Temporal knowledge graph reasoning (TKGR) is crucial for capturing dynamic relational dependencies and inferring evolving facts. However, existing embedding-based and diffusion-based methods primarily rely on Euclidean point embeddings and face two limitations: (1) sparse entities may suffer from embedding crowding and norm-sensitive scoring, especially under limited supervision in long-tail temporal knowledge graphs; (2) uniform noise schedules in diffusion models ignore temporal heterogeneity and instance-level prediction difficulty. To address these challenges, we propose SimDiff-DNS (Simplex Diffusion with Dynamic Noise Scheduling), a simplex-anchored logit diffusion framework for TKGR. First, we represent entity states as probability distributions on the simplex and obtain continuous embeddings as convex combinations of learnable entity basis vectors. This simplex-coordinate parameterization provides a probabilistic view of uncertainty and alleviates norm-sensitive ranking behavior for sparse entities. Second, we introduce a difficulty-aware dynamic noise scheduling strategy for the training corruption process, which adjusts the noise applied to target-entity logits according to a bounded difficulty score. Extensive experiments on three TKGR datasets show that SimDiff-DNS consistently improves over the diffusion-based baseline (improving MRR by 3.25 points on ICEWS14) and achieves competitive or state-of-the-art results on several metrics. Additional diagnostic analyses further demonstrate its benefits for long-tail entities, calibration, and ranking stability.

Temporal knowledge graph (TKG) reasoning, a central task in temporal knowledge representation, focuses on predicting future facts by leveraging historical temporal contexts. However, current approaches face two major challenges: limited generalization to unseen facts and insufficient interpretability of reasoning processes. To address these challenges, this paper proposes the Denoising Logic-based Temporal Knowledge Graph (DLTKG) framework, which employs a denoising diffusion process to complete reasoning tasks by introducing a noise source and a historical conditionguiding mechanism. Specifically, DLTKG constructs fuzzy entity representations by treating historical facts as noise sources, thereby enhancing the semantic associations between entities and the generalization ability for unseen facts. Additionally, the condition-based guidance mechanism, rooted in the relationship evolutionary paths, is designed to improve the interpretability of the reasoning process. Furthermore, we introduce a fine-tuning strategy that optimizes the denoising process by leveraging shortest path information between the head entity and candidate entities. Experimental results on three benchmark datasets demonstrate that DLTKG outperforms state-of-the-art methods across multiple evaluation metrics. Our code is available at: https://github.com/NEU-IDKE/DLTKG