Your Model Diversity, Not Method, Determines Reasoning Strategy

Compute scaling for LLM reasoning requires allocating budget between exploring solution approaches ($breadth$) and refining promising solutions ($depth$). 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 $\mathbf{\text{the}}\mathbf{\text{optimal}}\mathbf{\text{strategy}}\mathbf{\text{depends}}\mathbf{\text{on}}\mathbf{\text{the}}\mathbf{\text{model’s}}\mathbf{\text{diversity}}\mathbf{\text{profile,}}\mathbf{\text{the}}\mathbf{\text{spread}}\mathbf{\text{of}}\mathbf{\text{probability}}\mathbf{\text{mass}}\mathbf{\text{across}}\mathbf{\text{solution}}\mathbf{\text{approaches,}}\mathbf{\text{and}}\mathbf{\text{that}}\mathbf{\text{this}}\mathbf{\text{must}}\mathbf{\text{be}}\mathbf{\text{characterized}}\mathbf{\text{before}}\mathbf{\text{any}}\mathbf{\text{exploration}}\mathbf{\text{strategy}}\mathbf{\text{is}}\mathbf{\text{adopted.}}$ 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.