Machine learning is increasingly used to model complex natural science data, such as DNA-stabilized silver nanoclusters (Ag_N-DNAs), where DNA sequences dictate structural and optical properties. Previous studies overlooked multi-dimensional features by focusing only on single-peak spectra. To address this, a novel generative framework combining Variational Autoencoders (VAEs) and Graph Neural Networks (GNNs) is proposed to encode and generate data while preserving complex geometric features in the latent space. The model effectively organizes biological sequences by leveraging domain-specific metrics to build a similarity graph, ensuring sequences with similar properties remain close. Tested on DNA and peptide datasets, the framework shows high reconstruction accuracy and improved clustering of sequences with shared biological traits. Hyperparameter tuning with Optuna further optimizes performance, offering a robust tool for designing and analyzing biological sequences in various scientific applications.