Drug addiction is a global public health crisis, and the design of antiaddiction drugs remains a major challenge due to intricate mechanisms. Since experimental drug screening and optimization are too time-consuming and expensive, there is urgent need to develop innovative artificial intelligence (AI) methods for addressing the challenge. We tackle this challenge by topology-inferred drug addiction learning (TIDAL) built from integrating multiscale topological Laplacians, deep bidirectional transformer, and ensemble-assisted neural networks (EANNs). Multiscale topological Laplacians are a novel class of algebraic topology tools that embed molecular topological invariants and algebraic invariants into its harmonic spectra and nonharmonic spectra, respectively. These invariants complement sequence information extracted from a bidirectional transformer. We validate the proposed TIDAL framework on 22 drug addiction related, 4 hERG, and 12 DAT data sets, which suggests that the proposed TIDAL is a state-of-the-art framework for the modeling and analysis of drug addiction data. We carry out cross-target analysis of the current drug addiction candidates to alert their side effects and identify their repurposing potentials. Our analysis reveals drug-mediated linear and bilinear target correlations. Finally, TIDAL is applied to shed light on relative efficacy, repurposing potential, and potential side effects of 12 existing antiaddiction medications. Our results suggest that TIDAL provides a new computational strategy for pressingly needed antisubstance addiction drug development.