This paper presents a deep learning generative model (GM) for crystal structure prediction (CSP) using a conditional crystal diffusion variational autoencoder (Cond-CDVAE). The model is designed to generate physically plausible crystal structures under diverse pressure conditions without requiring local optimization. The Cond-CDVAE is trained on a comprehensive dataset containing over 670,000 local minimum structures, including both high-pressure and ambient-pressure structures from the Materials Project database. The model demonstrates high-fidelity generation, achieving an accuracy rate of 59.3% for 3,547 unseen ambient-pressure experimental structures within 800 samplings, and an accuracy rate of 83.2% for structures with fewer than 20 atoms per unit cell. These results surpass those of conventional CSP methods based on global optimization, showcasing the potential of GMs in CSP. The study also highlights the importance of integrating physical constraints, such as space group symmetry, into GMs to enhance their performance in predicting complex crystal structures.This paper presents a deep learning generative model (GM) for crystal structure prediction (CSP) using a conditional crystal diffusion variational autoencoder (Cond-CDVAE). The model is designed to generate physically plausible crystal structures under diverse pressure conditions without requiring local optimization. The Cond-CDVAE is trained on a comprehensive dataset containing over 670,000 local minimum structures, including both high-pressure and ambient-pressure structures from the Materials Project database. The model demonstrates high-fidelity generation, achieving an accuracy rate of 59.3% for 3,547 unseen ambient-pressure experimental structures within 800 samplings, and an accuracy rate of 83.2% for structures with fewer than 20 atoms per unit cell. These results surpass those of conventional CSP methods based on global optimization, showcasing the potential of GMs in CSP. The study also highlights the importance of integrating physical constraints, such as space group symmetry, into GMs to enhance their performance in predicting complex crystal structures.