Your Model Diversity, Not Method, Determines Reasoning Strategy

Compute scaling for LLM reasoning requires allocating budget between exploring solution approaches (\emph{breadth}) and refining promising solutions (\emph{depth}). Most methods implicitly trade off one for the other, yet why a given trade-off works remains unclear, and validation on a single model obscures the role of the model itself. We argue that \textbf{the optimal strategy depends on the model's \emph{diversity profile}, the spread of probability mass across solution approaches, and that this must be characterized before any exploration strategy is adopted.} We formalize this through a theoretical framework decomposing reasoning uncertainty and derive conditions under which tree-style depth refinement outperforms parallel sampling. We validate it on Qwen-3 4B and Olmo-3 7B families, showing that lightweight signals suffice for depth-based refinement on low-diversity aligned models while yielding limited utility for high-diversity base models, which we hypothesize require stronger compensation for lower exploration coverage.