Large Reasoning Models (LRMs) benefit substantially from training on challenging competition-level questions. However, existing automated question synthesis methods lack precise difficulty control, incur high computational costs, and struggle to generate competition-level questions at scale. In this paper, we propose CoDiQ (Controllable Difficult Question Generation), a novel framework enabling fine-grained difficulty control via test-time scaling while ensuring question solvability. Specifically, first, we identify a test-time scaling tendency (extended reasoning token budget boosts difficulty but reduces solvability) and the intrinsic properties defining the upper bound of a model's ability to generate valid, high-difficulty questions. Then, we develop CoDiQ-Generator from Qwen3-8B, which improves the upper bound of difficult question generation, making it particularly well-suited for challenging question construction. Building on the CoDiQ framework, we build CoDiQ-Corpus (44K competition-grade question sequences). Human evaluations show these questions are significantly more challenging than LiveCodeBench/AIME with over 82% solvability. Training LRMs on CoDiQ-Corpus substantially improves reasoning performance, verifying that scaling controlled-difficulty training questions enhances reasoning capabilities. We open-source CoDiQ-Corpus, CoDiQ-Generator, and implementations to support related research.

翻译：大型推理模型（LRM）通过训练于具有挑战性的竞赛级问题而显著受益。然而，现有的自动化问题合成方法缺乏精确的难度控制，计算成本高昂，且难以大规模生成竞赛级问题。本文提出CoDiQ（可控难度问题生成），这是一个新颖的框架，通过测试时缩放实现细粒度难度控制，同时确保问题的可解性。具体而言，首先，我们识别出一种测试时缩放趋势（扩展的推理令牌预算会提升难度但降低可解性），以及定义模型生成有效高难度问题能力上限的内在属性。然后，我们从Qwen3-8B开发了CoDiQ-Generator，它提升了生成高难度问题的能力上限，使其特别适合构建具有挑战性的问题。基于CoDiQ框架，我们构建了CoDiQ-Corpus（包含44K条竞赛级问题序列）。人工评估表明，这些问题比LiveCodeBench/AIME中的问题显著更具挑战性，且可解性超过82%。在CoDiQ-Corpus上训练LRM能大幅提升推理性能，验证了扩展可控难度训练问题可增强推理能力。我们开源了CoDiQ-Corpus、CoDiQ-Generator及相关实现，以支持相关研究。