In this paper, we explore the potential of artificial intelligence (AI) to address the challenges posed by terahertz ultra-massive multiple-input multiple-output (THz UM-MIMO) systems. We begin by outlining the characteristics of THz UM-MIMO systems, and identify three primary challenges for the transceiver design: 'hard to compute', 'hard to model', and 'hard to measure'. We argue that AI can provide a promising solution to these challenges. We then propose two systematic research roadmaps for developing AI algorithms tailored for THz UM-MIMO systems. The first roadmap, called model-driven deep learning (DL), emphasizes the importance to leverage available domain knowledge and advocates for adopting AI only to enhance the bottleneck modules within an established signal processing or optimization framework. We discuss four essential steps to make it work, including algorithmic frameworks, basis algorithms, loss function design, and neural architecture design. Afterwards, we present a forward-looking vision through the second roadmap, i.e., physical layer foundation models. This approach seeks to unify the design of different transceiver modules by focusing on their common foundation, i.e., the wireless channel. We propose to train a single, compact foundation model to estimate the score function of wireless channels, which can serve as a versatile prior for designing a wide variety of transceiver modules. We will also guide the readers through four essential steps, including general frameworks, conditioning, site-specific adaptation, and the joint design of foundation models and model-driven DL.

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