Database engines have historically absorbed many of the innovations in data processing, adding features to process graph data, XML, object oriented, and text among many others. In this paper, we make the case that it is time to do the same for AI -- but with a twist! While existing approaches have tried to achieve this by integrating databases with external ML tools, in this paper we claim that achieving a truly AI-centric database requires moving the DBMS engine, at its core, from a relational to a tensor abstraction. This allows us to: (1) support multi-modal data processing such as images, videos, audio, text as well as relational; (2) leverage the wellspring of innovation in HW and runtimes for tensor computation; and (3) exploit automatic differentiation to enable a novel class of "trainable" queries that can learn to perform a task. To support the above scenarios, we introduce TDP: a system that builds upon our prior work mapping relational queries to tensors. Thanks to a tighter integration with the tensor runtime, TDP is able to provide a broader coverage of new emerging scenarios requiring access to multi-modal data and automatic differentiation.