通过多样化采样提升大模型推理性能，理论揭示其增效机制。

Large language model (LLM) scaling inference is key to unlocking greater performance, and leveraging diversity has proven an effective way to enhance it. Motivated by the observed relationship between solution accuracy and meaningful response diversity, we systematically study the effect of prompt diversity in scaling inference. We theoretically explain why diversified sampling improves Best-of-$N$ scaling, showing that responses generated from diverse prompts after Best-of-$N$ selection exhibit significantly lower error rates than those produced from stationary prompts. Building on this analysis, we derive a diversity-fidelity trade-off principle, that guides the design of sampling strategies introducing diversity. From this guidance, we instantiate a family of effective perturbation styles. We theoretically and empirically characterize \textbf{when} diversified exploration remains effective, demonstrating that it works under a variety of conditions, and we further show that under majority voting, diversity may vanish. Finally, we systematically evaluate the effectiveness of sampling diversity and show that, when applied appropriately in different contexts, meaningful perturbations yield stronger, task-dependent gains as diversity increases. Overall, this work provides a systematic analysis that offers a theoretical and empirical foundation for understanding how sampling diversity affects LLM inference-time scaling.