The continual evolution of SARS-CoV-2 and the emergence of variants that show resistance to vaccines and neutralizing antibodies threaten to prolong the COVID-19 pandemic. Selection and emergence of SARS-CoV-2 variants are driven in part by mutations within the viral spike protein and in particular the ACE2 receptor-binding domain (RBD), a primary target site for neutralizing antibodies. Here, we develop deep mutational learning (DML), a machine-learning-guided protein engineering technology, which is used to investigate a massive sequence space of combinatorial mutations, representing billions of RBD variants, by accurately predicting their impact on ACE2 binding and antibody escape. A highly diverse landscape of possible SARS-CoV-2 variants is identified that could emerge from a multitude of evolutionary trajectories. DML may be used for predictive profiling on current and prospective variants, including highly mutated variants such as Omicron, thus guiding the development of therapeutic antibody treatments and vaccines for COVID-19.