Prior approaches to generating diverse plans in domain-independent planning seek out variations on plan structure such as actions or causal links used, or states entered. Measuring such syntactic differences between plans can be misleading because syntactically different plans can be semantically identical. We develop a landmark-based plan distance measure that captures semantic differences between plans.The landmark-based distance measure focuses on the disjunctive landmarks satisfied by each plan. We develop a simple algorithm for finding diverse plans that is based upon the LAMA planner. We illustrate that, in comparison with plan distance measures, landmark-based plan distance is not as susceptible to including irrelevant or redundant actions in plans to increase plan distance. Through extensive empirical evaluation, we find that high landmark distance between plans implies high action set distance, but not vice versa. Landmark-based plan distance overcomes some of the weaknesses of syntactic plan distance measures and can be used to find plan sets that are both landmark diverse and action set diverse.