The adoption of machine learning in materials science has rapidly transformed materials property prediction. Hurdles limiting full capitalization of recent advancements in machine learning include the limited development of methods to learn the underlying interactions of multiple elements, as well as the relationships among multiple properties, to facilitate property prediction in new composition spaces. To address these issues, we introduce the Hierarchical Correlation Learning for Multi-property Prediction (H-CLMP) framework that seamlessly integrates (i) prediction using only a material’s composition, (ii) learning and exploitation of correlations among target properties in multitarget regression, and (iii) leveraging training data from tangential domains via generative transfer learning. The model is demonstrated for prediction of spectral optical absorption of complex metal oxides spanning 69 3-cation metal oxide composition spaces. H-CLMP accurately predicts non-linear composition-property relationships in composition spaces for which no training data is available, which broadens the purview of machine learning to the discovery of materials with exceptional properties. This achievement results from the principled integration of latent embedding learning, property correlation learning, generative transfer learning, and attention models. The best performance is obtained using H-CLMP with Transfer learning (H-CLMP(T)) wherein a generative adversarial network is trained on computational density of states data and deployed in the target domain to augment prediction of optical absorption from composition. H-CLMP(T) aggregates multiple knowledge sources with a framework that is well-suited for multi-target regression across the physical sciences.