Recently, Generative Recommenders (GRs) have emerged as a transformative recommendation paradigm by replacing traditional item IDs with semantic indices (SIDs). Owing to the exceptional generative capabilities of diffusion models, a few pioneering works explore developing GRs with diffusion architectures as the backbone. However, a fatal limitation of existing diffusion-based GRs is that the diffusion process applies uniformly to all items within the historical interactions. In contrast, the user preference is shaped by multifaceted time-evolving factors and thus exhibits a non-stationary distribution in the temporal aspect. To bridge this gap, this study proposes a novel GR framework, named TDPM, by designing the time-aware diffusion on SID tokens. Specifically, TDPM explicitly integrates the impact of time-evolving user preferences into the diffusion process. In detail, the user preference is disentangled into (i) the period preference, which remains consistent over a long time-span, and (ii) the point preference, which is triggered by recent focal events. Extensive experiments on three public real-world datasets demonstrate the significant superiority of TDPM over the state-of-the-art baselines. TDPM achieves average improvements of up to 29.21% and 25.45% in terms of HR@20 and NDCG@20, respectively. The ablation study further underscores the necessity of time-aware token diffusion in diffusion-based GRs.