Piezoelectric metamaterials are a class of composite structural materials with a piezoelectric effect that achieve efficient coupling between electrical and mechanical energy through their unique microscopic design. Typically, the tailoring of cellular architectures paves the way for unlocking the potential to achieve unprecedentedly designed materials with specific properties. We have developed three different inverse design frameworks for metamaterials, using deep learning (DL) techniques and underpinned by Bayesian optimization. These frameworks reveal precise one-to-many correlations between material properties and geometric parameters within the triple periodic minimal surface (TPMS) piezoelectric metamaterial. For the first time, we have introduced the Progressive Latin Hypercube Sampling (PLHS) method to the inverse design process of metamaterials, highlighting the effectiveness of uniform sampling to improve the efficiency of deep learning models. The conditional variational autoencoder (cVAE), the conditional generative adversarial network (cGAN) and the multilayer perceptron (MLP) are studied for comparative analysis. All three models incorporate an inverse design network and a feature predictor to construct a continuous latent representation of a large number of hybrid TPMS (H-TPMS). After extensive training, the models can generate various piezoelectric porous structures that accurately meet the required material property parameters. Our results demonstrate the high accuracy of cVAE in inverse design, with 98.92% agreement for piezoelectric values and 96.44% agreement for mechanical properties. The three inverse design frameworks show different generalization capabilities, with cVAE performing best. This study thoroughly analyses the strengths and limitations of each model, providing valuable insights for researchers seeking inverse design recommendations.