Abstract: We study the problem of $\text{\emph{vector set search}}$ with $\text{\emph{vector set queries}}$. This task is analogous to traditional near-neighbor search, with the exception that both the query and each element in the collection are $\text{\textit{sets}}$ of vectors. We identify this problem as a core subroutine for semantic search applications and find that existing solutions are unacceptably slow. Towards this end, we present a new approximate search algorithm, DESSERT ($\text{\bf D}$ESSERT $\text{\bf E}$ffeciently $\text{\bf S}$earches $\text{\bf S}$ets of $\text{\bf E}$mbeddings via $\text{\bf R}$etrieval $\text{\bf T}$ables). DESSERT is a general tool with strong theoretical guarantees and excellent empirical performance. When we integrate DESSERT into ColBERT, a state-of-the-art semantic search model, we find a 2-5x speedup on the MS MARCO and LoTTE retrieval benchmarks with minimal loss in recall, underscoring the effectiveness and practical applicability of our proposal.