Temporal Knowledge Graph (TKG) reasoning seeks to predict future missing facts from historical evidence. While diffusion models (DM) have recently gained attention for their ability to capture complex predictive distributions, two gaps remain: (i) the generative path is conditioned only on positive evidence, overlooking informative negative context, and (ii) training objectives are dominated by cross-entropy ranking, which improves candidate ordering but provides little supervision over the calibration of the denoised embedding. To bridge this gap, we introduce Negative-Aware Diffusion model for TKG Extrapolation (NADEx). Specifically, NADEx encodes subject-centric histories of entities, relations and temporal intervals into sequential embeddings. NADEx perturbs the query object in the forward process and reconstructs it in reverse with a Transformer denoiser conditioned on the temporal-relational context. We further derive a cosine-alignment regularizer derived from batch-wise negative prototypes, which tightens the decision boundary against implausible candidates. Comprehensive experiments on four public TKG benchmarks demonstrate that NADEx delivers state-of-the-art performance.