The increasing use of generative models such as diffusion models for synthetic data augmentation has greatly reduced the cost of data collection and labeling in downstream perception tasks. However, this new data source paradigm may introduce important security concerns. This work investigates backdoor propagation in such emerging generative data supply chains, namely Data-Chain Backdoor (DCB). Specifically, we find that open-source diffusion models can become hidden carriers of backdoors. Their strong distribution-fitting ability causes them to memorize and reproduce backdoor triggers during generation, which are subsequently inherited by downstream models, resulting in severe security risks. This threat is particularly concerning under clean-label attack scenarios, as it remains effective while having negligible impact on the utility of the synthetic data. Furthermore, we discover an Early-Stage Trigger Manifestation (ESTM) phenomenon: backdoor trigger patterns tend to surface more explicitly in the early, high-noise stages of the diffusion model's reverse generation process before being subtly integrated into the final samples. Overall, this work reveals a previously underexplored threat in generative data pipelines and provides initial insights toward mitigating backdoor risks in synthetic data generation.