Multi-agent path finding (MAPF) represents a task of finding non-colliding paths for agents via which they can navigate from their initial positions to specified goal positions. Contemporary optimal solving algorithms include dedicated search-based methods, that solve the problem directly, and compilation-based algorithms that reduce MAPF to a different formalism for which an efficient solver exists. In this paper, we enhance the existing Boolean satisfiability-based (SAT) algorithm for MAPF via using sparse decision diagrams representing the set of candidate paths for each agent, from which the target Boolean encoding is derived, considering more promising paths before the less promising ones are taken into account. Suggested sparse diagrams lead to a smaller target Boolean formulae that can be constructed and solved faster while optimality guarantees of the approach are kept. Specifically, considering the candidate paths sparsely instead of considering them all makes the SAT-based approach more competitive for MAPF on large maps.