Sequential recommendation predicts the next items a user will interact with by modeling evolving preferences over time. Recent diffusion-based generative recommenders show promise in capturing complex dependencies, but they typically treat temporal context as an external conditioning signal rather than integrating temporal transitions into the diffusion dynamics. In this paper, we introduce TDRec (Temporally-aware Diffusion for sequential Recommendation), a novel framework that integrates temporal progression into both forward and reverse processes: at each diffusion step, a position's latent is updated by noise injection and by mixing with its preceding latent. We derive a closed-form solution for this temporal mixing process, proving that it allows for efficient parallel training with O(1) complexity relative to sequence length. Furthermore, we establish the existence of a corresponding DDPM-like reverse process and a reparameterized objective, ensuring efficient optimization and sampling without incurring extra computational overhead. Empirical results on three public datasets demonstrate that TDRec consistently outperforms state-of-the-art baselines, including recent diffusion models. Ablation studies confirm the effectiveness of the temporal scheduler and sequence-reduction module in generating coherent, context-aware predictions. Code is available at https://github.com/wuyaoericyy/TDRec.