Inverse problems, where the objective is to infer input parameters from observed properties, are common across scientific and engineering disciplines. In the absence of analytical determinations or computationally efficient numerical approximations, solving an inverse problem often requires extensive computational resources to make observations from known input parameters and sufficiently explore the space of possible parameters. This dissertation proposes several novel multi-fidelity active learning approaches to help address this high computational cost while dynamically balancing trade-offs of accuracy and efficiency. The algorithms introduced fall into two broad categories. The first category of algorithms excels at interfacing with other AI-driven models to navigate through a large and complex state space to identify non-unique candidate solutions to inverse problems. The second category of algorithms excels at repeatedly selecting from within a more compact state space with the objective of identifying a unique, or near-unique, solution to an inverse problem. Taken together, we demonstrate that these algorithms can improve the navigation and multi-fidelity measurement capabilities of computational and experimental workflows to accelerate scientific discovery.