Vocal music is an art about the perception and expression of sound. Successful vocal music teaching is to cultivate students’ unique singing personality, so this paper constructs a personalized vocal music teaching mode with the help of AI algorithm. Subsequently, it describes the problem of service object learners under personalized learning path recommendation, proposes a personalized learning path recommendation strategy based on ant colony optimization algorithm, and verifies the recommendation effect of personalized path through simulation experiments. Then the cognitive diagnosis model based on KM-VDINA is proposed to diagnose students’ vocal music knowledge under personalized learning path. The article concludes through experiments that the personalized vocal music teaching model based on AI algorithms requires the integration of online and offline teaching, while focusing on the integration of teaching inside and outside the classroom. The vocal music learning path of most students can be expressed as (000000)→(100001)→(101001)→(101100)→(111100)→(101110)→(111111). Students have multiple trajectories to master the attributes of vocal music knowledge, so teachers can explain the attributes of knowledge that are easier to master according to the actual situation, and then explain the attributes of knowledge that are difficult for students to master.