CoDiQ: Test-Time Scaling for Controllable Difficult Question Generation

TL;DR

CoDiQ tackles the challenge of scaling training data for large reasoning models by enabling fine-grained difficulty control through test-time scaling, while preserving solvability. The framework combines six Difficulty-Enhancement Strategies, a hybrid Difficulty Estimation (LLM rankings and a ValueNetwork), and a solvability verifier within an iterative CoDiQ Pipeline that evolves questions across up to eight rounds. A reinforcement-learning–driven CoDiQ-Generator is trained on boundary cases, enabling higher difficulty while maintaining validity, and the resulting CoDiQ-Corpus contains about 44K competition-grade math and coding questions. Human evaluation and curriculum-learning experiments show that training on CoDiQ-Corpus substantially improves reasoning performance, with questions that are significantly harder than existing benchmarks but still solvable, and the authors open-source the corpus, generator, and implementations. Overall, CoDiQ provides a scalable, controllable path to frontier reasoning data, though it faces limitations from the verifier capacity and a language scope currently restricted to English math/code tasks.

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.

Figures (7)

• Figure 1: Distribution of CoDiQ-Corpus Dataset
• Figure 2: Question Difficulty Scaling on CoDiQ-Bench. Scatter plot showing the relationship between average reasoning tokens and difficulty ranking (DR-AVG) for models using CoDiQ Prompt. Each point represents a model, demonstrating the positive correlation between increased reasoning computation and generated problem difficulty.
• Figure 3: Model Performance on CoDiQ-Bench Across Token Budgets. Average difficulty rank (%) of three model variants (Qwen3-8B with Direct Prompt, Qwen3-8B with CoDiQ Prompt, and CoDiQ-Gen-8B) under different token budget constraints (8k, 16k, 32k). Higher scores indicate better performance in handling difficult questions.
• Figure 4: Question Difficulty Scaling on CoDiQ-Bench. Normalized average difficulty ranking of questions generated by different Long-CoT models across 8 rounds. Higher rankings indicate higher question difficulty and better model performance.
• Figure 5: Question Solvability Scaling on CoDiQ-Bench. Solvable rate of questions generated by different Long-CoT models across 8 rounds. Higher indicates indicate better question quality.