The paper introduces Con-CDVAE, an extension of the Crystal Diffusion Variational Autoencoder (CDVAE) for conditional crystal generation. The authors propose innovative components, a two-step training method, and three unique generation strategies to enhance model performance. The effectiveness of Con-CDVAE is demonstrated through extensive testing under various conditions, including single and combined property targets. Ablation studies highlight the critical role of new components in achieving the model's performance. The physical credibility of the generated crystals is validated using Density Functional Theory (DFT) calculations, confirming the potential of Con-CDVAE in material science research. The method involves a diffusion model and a crystal generative model, with the diffusion model used to generate crystals and the latent variables of crystals. The Con-CDVAE model includes the *Prop_{Emb}* and *Predictor* blocks for conditional generation, inspired by DALL-E2. The *Prior* block, based on the DDPM version of the diffusion model, generates latent variables with given properties. The model is trained in two steps: first, the *Encoder*, *Predictor*, *Prop_{Emb}*, and *Decoder* are trained using a joint loss function; second, the *Prior* block is trained using default and full condition *Prior*. Experiments show that Con-CDVAE performs well in regions with sufficient data but can also generate crystals in regions with insufficient data. Ablation experiments demonstrate the importance of the *Predictor* block in building the spatial structure of latent variables. DFT validation confirms the rationality of the generated crystals, showing that Con-CDVAE can generate crystals based on target properties and outside the training set. The paper concludes by discussing areas for further improvement, such as recognizing symmetry information and reducing the mean absolute change (MAC) and root mean squared displacement (RMSD) of generated crystals before and after relaxation.The paper introduces Con-CDVAE, an extension of the Crystal Diffusion Variational Autoencoder (CDVAE) for conditional crystal generation. The authors propose innovative components, a two-step training method, and three unique generation strategies to enhance model performance. The effectiveness of Con-CDVAE is demonstrated through extensive testing under various conditions, including single and combined property targets. Ablation studies highlight the critical role of new components in achieving the model's performance. The physical credibility of the generated crystals is validated using Density Functional Theory (DFT) calculations, confirming the potential of Con-CDVAE in material science research. The method involves a diffusion model and a crystal generative model, with the diffusion model used to generate crystals and the latent variables of crystals. The Con-CDVAE model includes the *Prop_{Emb}* and *Predictor* blocks for conditional generation, inspired by DALL-E2. The *Prior* block, based on the DDPM version of the diffusion model, generates latent variables with given properties. The model is trained in two steps: first, the *Encoder*, *Predictor*, *Prop_{Emb}*, and *Decoder* are trained using a joint loss function; second, the *Prior* block is trained using default and full condition *Prior*. Experiments show that Con-CDVAE performs well in regions with sufficient data but can also generate crystals in regions with insufficient data. Ablation experiments demonstrate the importance of the *Predictor* block in building the spatial structure of latent variables. DFT validation confirms the rationality of the generated crystals, showing that Con-CDVAE can generate crystals based on target properties and outside the training set. The paper concludes by discussing areas for further improvement, such as recognizing symmetry information and reducing the mean absolute change (MAC) and root mean squared displacement (RMSD) of generated crystals before and after relaxation.