Recent advances in machine learning methods have had a significant impact on protein structure prediction, but accurate generation and characterization of protein-folding pathways remains intractable. Here, we demonstrate how protein folding trajectories can be generated using a directed walk strategy operating in the space defined by the residue-level contact-map. This double-ended strategy views protein folding as a series of discrete transitions between connected minima on the potential energy surface. Subsequent reaction-path analysis for each transition enables thermodynamic and kinetic characterization of each protein-folding path. We validate the protein-folding paths generated by our discretized-walk strategy against direct molecular dynamics simulations for a series of model coarse-grained proteins constructed from hydrophobic and polar residues. This comparison demonstrates that ranking discretized paths based on the intermediate energy barriers provides a convenient route to identifying physically sensible folding ensembles. Importantly, by using directed walks in the protein contact-map space, we circumvent several of the traditional challenges associated with protein-folding studies, namely, long time scales required and the choice of a specific order parameter to drive the folding process. As such, our approach offers a useful new route for studying the protein-folding problem.