Cognitive diagnosis (CD) aims to assess students’ mastery of specific knowledge concepts and problems. However, cold-start scenarios in intelligent educational systems pose critical challenges due to the scarcity of student-course interaction records. To address this issue, this study introduces the Correlation-aware Cold-start Cognitive Diagnosis (CCCD) framework, which integrates multi-source heterogeneous information to model inter-course relationships. The proposed framework leverages three complementary modalities, namely student performance records, syllabus-level semantic content, and course knowledge graphs, to construct a multidimensional course correlation matrix. An entropy-based weighting mechanism is employed to adaptively balance their contributions, yielding a robust prior matrix that captures cross-modal dependencies. This matrix is further incorporated into an attention-based knowledge transfer module, enabling accurate estimation of cognitive states in data-scarce target courses. Extensive experiments on large-scale real-world educational datasets demonstrate that CCCD consistently outperforms state-of-the-art baseline methods. Moreover, ablation studies highlight the critical role of multi-modal correlation modeling in improving both diagnostic precision and model robustness.