A Model of Diverse Sampling from Language Models

Language models often produce high-quality individual samples but poor sets, with repeated samples clustering around the same semantic modes. We formalize diverse generation as sampling a size-$K$ subset of complete strings from a determinantal point process (DPP), where the likelihood encodes item quality, and the embedding geometry encodes repulsion between similar outputs. Exact inference over all strings is intractable, so we propose \algname: draw a finite candidate pool from a tractable proposal, importance-weight candidates toward a globally tempered quality distribution, and run either $K$-DPP sampling or greedy MAP selection on the induced pool kernel. We prove a finite-sample bound showing that the KL bias of the pooled sampler decays as $\mathcal{O}(1/N)$ in the pool size. Empirically, \algname improves the quality--diversity Pareto frontier over temperature sampling, diverse beam search, $K$-means reranking, and LLM-based selection on open-ended generation, ambiguous text-to-SQL (Ambrosia), and mathematical reasoning (GSM8K) tasks.