CoDiQ: Test-Time Scaling for Controllable Difficult Question Generation

TL;DR

This paper introduces CoDiQ, a framework for controllable, test-time scaling of question difficulty in large reasoning models, enabling the generation of challenging, solvable questions that improve model reasoning performance.

Contribution

The paper presents CoDiQ, a novel method for fine-grained difficulty control in question generation, along with a large corpus and generator that enhance reasoning model training.

Findings

Generated questions are more challenging than existing benchmarks.

Training models on CoDiQ-Corpus improves reasoning performance.

CoDiQ enables scalable, controllable question difficulty at test time.

Abstract

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.