Generating multiple diverse and high-quality solutions is valuable for many applications, such as code-test generation and drug discovery. However, Large Language Models (LLMs) tend to converge on a single high-confidence solution during inference, limiting exploration of alternative valid solution paths. Existing test-time methods promote diversity through tree-like search and prune semantically similar branches using response-level semantic embeddings. However, we find that such embeddings are easily confounded by linguistic and stylistic similarities, making it difficult to distinguish genuinely distinct solution paths. To address this, we introduce Answer Probing, which probes the potential answer an LLM would reach from an intermediate reasoning path. We demonstrate that the hidden states of probed answers more effectively differentiate distinct solution paths than semantic embeddings, and the perplexity of probed answers serves as a practical proxy for reasoning correctness. Based on these findings, we propose Answer Probing-Guided Tree Search (APTS), which guides the tree search by the probed answers' hidden state similarity and perplexity. Experiments on three reasoning tasks across two LLMs show that APTS consistently enhances solution diversity, demonstrating its effectiveness and robustness.
Open-ended generation tasks often require a set of meaningfully different outputs, yet large language models often produce similar generations. Existing test-time diversity methods operate at different stages of generation with varying effectiveness, but it remains unclear what design choices lead to meaningful diversity in the output. We introduce a framework that characterizes test-time diverse generation methods by the diversity source introduced during generation and provide a transmission score for measuring how effectively variation in the source reaches the final output. Guided by this framework, we propose fully automated specification-level generation methods that first generate diverse intermediate specifications and then condition on them to produce final responses. Across five open-ended tasks and four backbone models, specification-level injection improves output diversity over test-time baselines while maintaining comparable quality. Our analysis shows that successful diversity injection depends on both the diversity of the sources and their transmission to the output, highlighting source design and source-to-output realization as two key levers for building more diverse generation systems.