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Objective: The rapid advancement of high-throughput technologies in the biomedical field has resulted in the accumulation of diverse omics data types, such as mRNA expression, DNA methylation, and microRNA expression, for studying various diseases. Integrating these multi-omics datasets enables a comprehensive understanding of the molecular basis of cancer and facilitates accurate prediction of disease progression. Methods: However, conventional approaches face challenges due to the dimensionality curse problem. This paper introduces a novel framework called Knowledge Distillation and Supervised Variational AutoEncoders utilizing View Correlation Discovery Network (KD-SVAE-VCDN) to address the integration of high-dimensional multi-omics data with limited common samples. Through our experimental evaluation, we demonstrate that the proposed KD-SVAE-VCDN architecture accurately predicts the progression of breast and kidney carcinoma by effectively classifying patients as long- or short-term survivors. Furthermore, our approach outperforms other state-of-the-art multi-omics integration models. Results: Our findings highlight the efficacy of the KD-SVAE-VCDN architecture in predicting the disease progression of breast and kidney carcinoma. By enabling the classification of patients based on survival outcomes, our model contributes to personalized and targeted treatments. The favorable performance of our approach in comparison to several existing models suggests its potential to contribute to the advancement of cancer understanding and management. Conclusion: The development of a robust predictive model capable of accurately forecasting disease progression at the time of diagnosis holds immense promise for advancing personalized medicine. By leveraging multi-omics data integration, our proposed KD-SVAE-VCDN framework offers an effective solution to this challenge, paving the way for more precise and tailored treatment strategies for patients with different types of cancer.