Personalized learning path optimization based on cognitive diagnosis models faces two key gaps: the sparsity of large-scale educational data makes it difficult for traditional DINA models to converge, and the psychological mechanism underlying the effectiveness of personalized paths lacks empirical testing. To address these gaps, this study proposes and validates a personalized learning path optimization framework that integrates Bayesian cognitive diagnosis, knowledge space theory, and cognitive load theory. The study employed a mixed-data design: in the first phase, a Bayesian DINA model was trained on the EdNet public dataset (N = 5,000) and a shortest remediation path algorithm was developed; in the second phase, a dataset with 120 students was used to validate the algorithm’s effectiveness, using the Bootstrap method to test the mediating effect of cognitive load and introducing a Hidden Markov Model to analyze the dynamic evolution of knowledge states. The results showed that the Bayesian DINA model converged successfully on data with 91.3% sparsity (R-hat < 1.01), with attribute mastery probability estimates ranging from 0.280 to 0.368; the personalized path improved efficiency by 23.6% compared to the fixed-order path (Cohen’s d = 0.98), which was cross-validated as a 22.0% time saving in a separate experiment involving probability learning; cognitive load was identified as the primary mediator between personalized paths and learning outcomes [indirect effect = 0.28, 95% CI (0.19, 0.37)], with learning motivation [indirect effect = 0.18, 95% CI (0.11, 0.25)] and self-efficacy [indirect effect = 0.12, 95% CI (0.06, 0.18)] serving as complementary mediators in a multiple mediation model. The three pathways together explained 86.6% of the total effect; the HMM identified A5 (Analytical Thinking) as a learning bottleneck, with a forward transition probability of only 0.31. This study provides a feasible methodological solution for cognitive diagnosis with sparse data, theoretically identifies the mediating pathway of cognitive load, and offers precise targets for bottleneck attribute intervention in intelligent tutoring systems in practice.