Metamaterials offer exceptional opportunities for designing lightweight structures with tailored mechanical properties; however, conventional design approaches typically rely on computationally intensive finite element analysis (FEA) and iterative optimization. Recent advances in generative artificial intelligence provide an alternative by learning compact latent representations capable of generating novel structural designs. In this work, we propose a Physics-Informed Conditional Variational Autoencoder (PI-CVAE) for the design and analysis of X-lattice metamaterials. A synthetic dataset of 10,000 parameterized X-lattice unit cells was generated as 64 × 64 binary images, with each sample annotated with beam angle, beam thickness, relative density, natural frequency, and compliance computed using an image-based beam finite element model. Unlike conventional CVAEs that optimize only image reconstruction, the proposed PI-CVAE jointly learns latent representations while simultaneously predicting mechanical properties through an auxiliary physics prediction network. This multi-task learning strategy encourages the latent space to capture both geometric and structural information. Experimental results demonstrate that the proposed approach significantly improves reconstruction quality, achieving an average mean squared error (MSE) of 0.000195, a peak signal-to-noise ratio (PSNR) of 44.47 dB, and a structural similarity index (SSIM) of 0.9984, substantially outperforming a standard CVAE. Latent-space visualizations further reveal well-organized continuous manifolds that preserve geometric characteristics while exhibiting strong correlation with structural frequency and compliance. These findings demonstrate that integrating physics-based supervision into generative models produces more informative latent representations and provides a promising framework for AI-assisted metamaterial design, inverse structural optimization, and lightweight engineering applications.