Achieving structural and stereogenic diversity from the same starting materials remains a fundamental challenge in organic synthesis, requiring precise control over the selectivity. Here, we report divergent catalytic methods that selectively yield either cycloaddition or addition/elimination products from bicyclo[1.1.0]butanes and α,β-unsaturated ketones. By employing chiral Lewis acid or Brønsted acid catalysts, we achieved excellent regio-, diastereo-, and enantioselectivity across all three distinct transformations, affording a diverse array of synthetically valuable chiral bicyclo[2.1.1]hexanes and cyclobutenes. The divergent outcomes are controlled by the differential activation of the substrates by the specific chiral catalyst with the reaction conditions dictating the pathway selectivity. This strategy demonstrates the power of divergent catalysis in creating molecular complexity and diversity, offering a valuable tool for the synthesis of enantioenriched chiral building blocks.