Unionable table search techniques input a query table from a user and search for data lake tables that can contribute additional rows to the query table. The definition of unionability is generally based on similarity measures which may include similarity between columns (e.g., value overlap or semantic similarity of the values in the columns) or tables (e.g., similarity of table embeddings). Due to this and the large redundancy in many data lakes (which can contain many copies and versions of the same table), the most unionable tables may be identical or nearly identical to the query table and may contain little new information. Hence, we introduce the problem of identifying unionable tuples from a data lake that are diverse with respect to the tuples already present in a query table. We perform an extensive experimental analysis of well-known diversity algorithms applied to this novel problem and identify a gap that we address with a novel, clustering-based tuple diversity algorithm called DUST. DUST uses a novel embedding model to represent unionable tuples that outperforms other tuple representation models by at least 15 % when representing unionable tuples. Using real data lake benchmarks, we show that our diversification algorithm is more than six times faster than the most efficient diversification baseline. We also show that it is more effective in diversifying unionable tuples than existing diversification algorithms.