Diffusion-Proof: Recipe for Formal Theorem Proving Beyond Auto-Regressive Generation

2026-06-17 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

Diffusion-Proof is presented as the first framework to train and apply diffusion Large Language Models (dLLMs) for formal theorem proving, addressing inherent limitations of auto-regressive (AR) LLMs in maintaining long-range coherence and compounding errors. This framework includes two distinct models: dLLM-Prover-7B, designed for whole-proof writing with long-range coherent tactic usage, and dLLM-Corrector-7B, a novel large block diffusion-based correction model leveraging in-filling capabilities for local proof correction using bi-directional information. Extensive experiments demonstrate Diffusion-Proof significantly outperforms AR LLM baselines trained on the same dataset, achieving an absolute improvement of 1.61% on ProofNet-Test and 6.14% on MiniF2F-Test benchmarks. Notably, Diffusion-Proof successfully resolved one IMO problem that the more advanced thinking model DeepSeek-Prover-V2-7B could not solve, showcasing dLLMs' unique advantages in this domain.

Key takeaway

For AI Scientists and Machine Learning Engineers developing advanced reasoning systems, Diffusion-Proof demonstrates that diffusion LLMs offer a superior approach to formal theorem proving compared to auto-regressive models. You should consider integrating dLLM architectures, like dLLM-Prover-7B and dLLM-Corrector-7B, to enhance long-range coherence and reduce error propagation in complex generative tasks. This method can significantly improve proof success rates, even on problems challenging models like DeepSeek-Prover-V2-7B.

Key insights

Diffusion-Proof applies dLLMs to formal theorem proving, outperforming AR models by leveraging iterative denoising for long-range coherence.

Principles

• Diffusion LLMs excel at long-range coherence.
• Bi-directional information improves proof correction.
• Iterative denoising mitigates error compounding.

Method

Diffusion-Proof trains dLLMs for formal theorem proving, using dLLM-Prover-7B for whole-proof generation and dLLM-Corrector-7B for local, bi-directional proof correction via iterative denoising.

In practice

• Apply dLLMs for complex sequence generation.
• Use diffusion for error correction tasks.
• Explore dLLMs for mathematical reasoning.

Topics

• Diffusion LLMs
• Formal Theorem Proving
• Mathematical Reasoning
• Proof Generation
• Error Correction
• Large Language Models

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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• Diffusion LLMs from the Ground Up: Training, Inference, and Practical Engineering — dLLMs offer competitive performance and significantly faster inference than AR models, especially when initialized from pre-trained AR checkpoints.
• Learning to Reason with Insight for Informal Theorem Proving — Teaching LLMs to identify core techniques significantly improves their informal theorem proving capabilities.
• Learning from the Self-future: On-policy Self-distillation for dLLMs — d-OPSD adapts self-distillation for dLLMs by using suffix conditioning and step-level supervision, significantly boosting sample efficiency.

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.