The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper takes the first step toward a rigorous analysis of multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory. Code is available at: \url{https://github.com/ML-GSAI/Multi-Source-GM}.

本研究解决了多数据源在条件生成建模中相互作用的理论不足问题。提出了一种基于包围数的平均总变差距离的条件最大似然估计的一般分布估计误差界限，表明当源分布具有相似性且模型表现力足够时，多源训练比单源训练具有更好的界限。模拟和实际实验验证了该理论的有效性。

多数据源条件生成建模理论