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This paper examines the theoretical performance of distributed diffusion models in environments where computational resources and data availability vary significantly among workers. Traditional models centered on single-worker scenarios fall short in such distributed settings, particularly when some workers are resource-constrained. This discrepancy in resources and data diversity challenges the assumption of accurate score function estimation foundational to single-worker models. We establish the inaugural generation error bound for distributed diffusion models in resource-limited settings, establishing a linear relationship with the data dimension $d$ and consistency with established single-worker results. Our analysis highlights the critical role of hyperparameter selection in influencing the training dynamics, which are key to the performance of model generation. This study provides a streamlined theoretical approach to optimizing distributed diffusion models, paving the way for future research in this area.