# ScaleDiff: Scaling Difficult Problems for Advanced Mathematical Reasoning

arXiv: https://arxiv.org/abs/2509.21070 · HTML: https://mlsanity.com/paper/2509.21070/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 56 of its 58 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 30 of 56)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Light-R1: Curriculum SFT, DPO and RL for Long COT from Scratch and Beyond](https://mlsanity.com/paper/2503.10460/) (2025)
- [AIMO-2 Winning Solution: Building State-of-the-Art Mathematical Reasoning Models with OpenMathReasoning dataset](https://mlsanity.com/paper/2504.16891/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Orca-Math: Unlocking the potential of SLMs in Grade School Math](https://mlsanity.com/paper/2402.14830/) (2024)
- [AdaptThink: Reasoning Models Can Learn When to Think](https://mlsanity.com/paper/2505.13417/) (2025)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)

## Built on by (most cited first, 6 of 6)

- [OpenDataArena: A Fair and Open Arena for Benchmarking Post-Training Dataset Value](https://mlsanity.com/paper/2512.14051/) (2025)
- [Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis](https://mlsanity.com/paper/2511.09907/) (2025)
- [Preventing Curriculum Collapse in Self-Evolving Reasoning Systems](https://mlsanity.com/paper/2603.13309/) (2026)
- [Tracing the Roots: A Multi-Agent Framework for Uncovering Data Lineage in Post-Training LLMs](https://mlsanity.com/paper/2604.10480/) (2026)
- [CoDiQ: Test-Time Scaling for Controllable Difficult Question Generation](https://mlsanity.com/paper/2602.01660/) (2026)
- [AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction](https://mlsanity.com/paper/2607.29549/) (2026)

## Abstract (arXiv)

Large Reasoning Models (LRMs) have shown impressive capabilities in complex problem-solving, often benefiting from training on difficult mathematical problems that stimulate intricate reasoning. Recent efforts have explored automated synthesis of mathematical problems by prompting proprietary models or large-scale open-source models from seed data or inherent mathematical concepts. However, scaling up these methods remains challenging due to their high computational/API cost, complexity of prompting, and limited difficulty level of the generated problems. To overcome these limitations, we propose ScaleDiff, a simple yet effective pipeline designed to scale the creation of difficult problems. We efficiently identify difficult problems from existing datasets with only a single forward pass using an adaptive thinking model, which can perceive problem difficulty and automatically switch between "Thinking" and "NoThinking" modes. We then train a specialized difficult problem generator (DiffGen-8B) on this filtered difficult data, which can produce new difficult problems in large scale, eliminating the need for complex, per-instance prompting and its associated high API costs. Fine-tuning Qwen2.5-Math-7B-Instruct on the ScaleDiff-Math dataset yields a substantial performance increase of 11.3% compared to the original dataset and achieves a 65.9% average accuracy on AIME'24, AIME'25, HMMT-Feb'25, BRUMO'25, and MATH500, outperforming recent strong LRMs like OpenThinker3. Notably, this performance is achieved using the cost-efficient Qwen3-8B model as a teacher, demonstrating that our pipeline can effectively transfer advanced reasoning capabilities without relying on larger, more expensive teacher models. Furthermore, we observe a clear scaling phenomenon in model performance on difficult benchmarks as the quantity of difficult problems increases. Code: https://github.com/QizhiPei/ScaleDiff.