Abstract: 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.

Lay Summary:

Diffusion models are widely used to generate high-quality data, but most theories assume that the training process is based on only one powerful machine with abundant data.In practice, diffusion models often need to be trained across many devices that differ widely in speed, memory and local datasets, breaking the usual guarantee of accurate score estimation on each worker. We address this by proving the first generation-error bound for diffusion models trained in such resource-limited, heterogeneous settings. Remarkably, our bound shows a linear relationship with the data dimension—matching the best known single-machine results. We also show how key hyperparameters (such as learning rates, noise schedules and update frequencies) directly influence this bound and hence the final generation quality. By tuning these settings, we can balance workloads across devices and still achieve reliable, high-quality output.