Deep learning compilers optimize DNN program execution by capturing them as operator-based computation graphs. However, developers’ deep learning programs often contain complex Python language features that prevent compilers from recognizing the entire program as a complete computation graph, resulting in sub-optimal performance. Our analysis reveals that actual capture failures involve only a few lines of code, we believe this problem can be addressed through code repair rather than extensive compiler improvements. To address this challenge, we introduce GraphGlue, a multi-agent system that leverages LLMs to repair and optimize DNN programs for compiler requirements, thereby maximizing the performance benefits of deep learning compilers. GraphGlue employs (1) graph-break cause mining (GCM) to identify hidden causes of computation graph breaks and facilitate LLM-based repair, and (2) self-correction with reject sampling (SRS) to alternate between code debugging and regeneration, effectively avoiding ineffective feedback attempts caused by incorrect initial optimization strategies. Experimental results demonstrate that programs optimized by GraphGlue achieve up to 2.19x (1.23x on average) speedup compared to using TorchDynamo directly, and deliver up to 15.77x (8.74x on average) memory savings compared to state-of-the-art AI compiler frontends. GraphGlue exhibits strong generalization capabilities across 1,411 real-world user programs, successfully optimizing 92.63% of them. Code is available at https://anonymous.4open.science/r/GraphGlue-5163/.