Integrating high-dimensional cellular multi-omics data is crucial for understanding various layers of biological control. Single 'omic methods provide important insights, but often fall short in handling the complex relationships between genes, proteins, metabolites and beyond. Here, we present a novel, non-linear, and unsupervised method called GAUDI (Group Aggregation via UMAP Data Integration) that leverages independent UMAP embeddings for the concurrent analysis of multiple data types. GAUDI uncovers non-linear relationships among different omics data better than several state-of-the-art methods. This approach not only clusters samples by their multi-omic profiles but also identifies latent factors across each omics dataset, thereby enabling interpretation of the underlying features contributing to each cluster. Consequently, GAUDI facilitates more intuitive, interpretable visualizations to identify novel insights and potential biomarkers from a wide range of experimental designs.