We introduce SAGE; a Generative LLM for inferring attribute values for products across world-wide e-Commerce catalogs. We introduce a novel formulation of the attribute-value prediction problem as a Seq2Seq summarization task, across languages, product types and target attributes. Our novel modeling approach lifts the restriction of predicting attribute values within a pre-specified set of choices, as well as, the requirement that the sought attribute values need to be explicitly mentioned in the text. SAGE can infer attribute values even when such values are mentioned implicitly using periphrastic language, or not-at-all-as is the case for common-sense defaults. Additionally, SAGE is capable of predicting whether an attribute is inapplicable for the product at hand, or non-obtainable from the available information. SAGE is the first method able to tackle all aspects of the attribute-value-prediction task as they arise in practical settings in e-Commerce catalogs. A comprehensive set of experiments demonstrates the effectiveness of the proposed approach, as well as, its superiority against state-of-the-art competing alternatives. Moreover, our experiments highlight SAGE's ability to tackle the task of predicting attribute values in zero-shot setting; thereby, opening up opportunities for significantly reducing the overall number of labeled examples required for training.