# MM-PRM: Enhancing Multimodal Mathematical Reasoning with Scalable Step-Level Supervision

arXiv: https://arxiv.org/abs/2505.13427 · HTML: https://mlsanity.com/paper/2505.13427/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 45 of its 65 references that are in the map.
- First posted on arXiv 19 May 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 45)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Qwen-VL: A Versatile Vision-Language Model for Understanding, Localization, Text Reading, and Beyond](https://mlsanity.com/paper/2308.12966/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [MiniCPM-V: A GPT-4V Level MLLM on Your Phone](https://mlsanity.com/paper/2408.01800/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Gemini: A Family of Highly Capable Multimodal Models](https://mlsanity.com/paper/2312.11805/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [The Lessons of Developing Process Reward Models in Mathematical Reasoning](https://mlsanity.com/paper/2501.07301/) (2025)
- [InternLM2 Technical Report](https://mlsanity.com/paper/2403.17297/) (2024)
- [Alphazero-like Tree-Search can Guide Large Language Model Decoding and Training](https://mlsanity.com/paper/2309.17179/) (2023)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)

## Built on by (most cited first, 30 of 31)

- [A Survey of Process Reward Models: From Outcome Signals to Process Supervisions for Large Language Models](https://mlsanity.com/paper/2510.08049/) (2025)
- [From Perception to Cognition: A Survey of Vision-Language Interactive Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2509.25373/) (2025)
- [A Survey on Agentic Multimodal Large Language Models](https://mlsanity.com/paper/2510.10991/) (2025)
- [GM-PRM: A Generative Multimodal Process Reward Model for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2508.04088/) (2025)
- [Training Vision-Language Process Reward Models for Test-Time Scaling in Multimodal Reasoning: Key Insights and Lessons Learned](https://mlsanity.com/paper/2509.23250/) (2025)
- [VRPRM: Process Reward Modeling via Visual Reasoning](https://mlsanity.com/paper/2508.03556/) (2025)
- [TIM-PRM: Verifying multimodal reasoning with Tool-Integrated PRM](https://mlsanity.com/paper/2511.22998/) (2025)
- [Unified Generation and Self-Verification for Vision-Language Models via Advantage Decoupled Preference Optimization](https://mlsanity.com/paper/2601.01483/) (2026)
- [VisioMath: Benchmarking Figure-based Mathematical Reasoning in LMMs](https://mlsanity.com/paper/2506.06727/) (2025)
- [StructVRM: Aligning Multimodal Reasoning with Structured and Verifiable Reward Models](https://mlsanity.com/paper/2508.05383/) (2025)
- [PaLMR: Towards Faithful Visual Reasoning via Multimodal Process Alignment](https://mlsanity.com/paper/2603.06652/) (2026)
- [Adversarial Training for Process Reward Models](https://mlsanity.com/paper/2511.22888/) (2025)
- [Advancing Multimodal Judge Models through a Capability-Oriented Benchmark and MCTS-Driven Data Generation](https://mlsanity.com/paper/2603.00546/) (2026)
- [MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling](https://mlsanity.com/paper/2605.12154/) (2026)
- [Training Data Efficiency in Multimodal Process Reward Models](https://mlsanity.com/paper/2602.04145/) (2026)
- [PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control](https://mlsanity.com/paper/2605.15963/) (2026)
- [Granularity-Regulated Adaptive Computational Efficiency for Optimal Verification in Test-Time Scaling](https://mlsanity.com/paper/2606.19354/) (2026)
- [VeriBound: PAC-Bayesian Generalization Bounds for Process Reward Models Trained with Formal Verification Tools](https://mlsanity.com/paper/2606.20740/) (2026)
- [Guided Verifier: Collaborative Multimodal Reasoning via Dynamic Process Supervision](https://mlsanity.com/paper/2602.04290/) (2026)
- [A Survey of Multimodal Mathematical Reasoning: From Perception, Alignment to Reasoning](https://mlsanity.com/paper/2603.08291/) (2026)
- [Process Rewards with Learned Reliability](https://mlsanity.com/paper/2605.15529/) (2026)
- [A Nash Equilibrium Framework For Training-Free Multimodal Step Verification](https://mlsanity.com/paper/2605.20033/) (2026)
- [IVR-R1: Refining Trajectories through Iterative Visual-Grounded Reasoning in Reinforcement Learning](https://mlsanity.com/paper/2605.23997/) (2026)
- [ProcessThinker: Enhancing Multi-modal Large Language Models Reasoning via Rollout-based Process Reward](https://mlsanity.com/paper/2606.11209/) (2026)
- [Before Thinking, Learn to Decide: Proactive Routing for Efficient Visual Reasoning](https://mlsanity.com/paper/2606.30217/) (2026)
- [VERDICT: Training-Free Step-Wise Verification of Multimodal Reasoning via Disagreement-Aware Consensus](https://mlsanity.com/paper/2608.10665/) (2026)
- [V-Rubrics: Visual Faithfulness via Rubric-Based Reinforcement Learning](https://mlsanity.com/paper/2608.25580/) (2026)
- [When LLM Meets Tree Search: A Systematic View of Inference as Search in Large Language Models](https://mlsanity.com/paper/2608.30395/) (2026)
- [HaPRL: Human-Anchored Process Reinforcement Learning for Visual Search Agent](https://mlsanity.com/paper/2609.37190/) (2026)
- [SPLIT-RL: Staged Perception-Language Reasoning Training with Claim-Level Advantages](https://mlsanity.com/paper/2610.10889/) (2026)

## Abstract (arXiv)

While Multimodal Large Language Models (MLLMs) have achieved impressive progress in vision-language understanding, they still struggle with complex multi-step reasoning, often producing logically inconsistent or partially correct solutions. A key limitation lies in the lack of fine-grained supervision over intermediate reasoning steps. To address this, we propose MM-PRM, a process reward model trained within a fully automated, scalable framework. We first build MM-Policy, a strong multimodal model trained on diverse mathematical reasoning data. Then, we construct MM-K12, a curated dataset of 10,000 multimodal math problems with verifiable answers, which serves as seed data. Leveraging a Monte Carlo Tree Search (MCTS)-based pipeline, we generate over 700k step-level annotations without human labeling. The resulting PRM is used to score candidate reasoning paths in the Best-of-N inference setup and achieves significant improvements across both in-domain (MM-K12 test set) and out-of-domain (OlympiadBench, MathVista, etc.) benchmarks. Further analysis confirms the effectiveness of soft labels, smaller learning rates, and path diversity in optimizing PRM performance. MM-PRM demonstrates that process supervision is a powerful tool for enhancing the logical robustness of multimodal reasoning systems. We release all our codes and data at https://github.com/ModalMinds/MM-PRM.