用扩散模型精准修复微分方程代码，速度快且准确。
DiffPDE: Masked Diffusion Language Models as PDE Solver
- 用局部重掩码和补全策略，只重生成错误部分。
- 在PDEBench上精度媲美、速度超越同规模自回归模型。
- 适合需要高效调试复杂微分方程代码的开发者。
现有求解偏微分方程（PDE）的合成方法主要依赖自回归模型，但其全局从左到右解码方式在处理本质局部性错误时存在大量冗余。本文提出DiffPDE框架，利用离散扩散语言模型实现目标化代码修复。通过引入局部重掩码与补全策略，DiffPDE仅重生成错误区域，同时保留正确上下文，自然契合PDE错误的稀疏特性。为应对需顺序干预的耦合错误，提出迭代调试GRPO（ID-GRPO），一种基于中间奖励的强化学习方案，支持单轨迹内多轮调试。在PDEBench上的实验表明，DiffPDE达到具有竞争力的精度，优于同等规模的自回归模型，并显著加速修复过程。
原文摘要 · Abstract (English)
Existing approaches for synthesizing Partial Differential Equation (PDE) solvers predominantly rely on autoregressive models, yet their global left-to-right decoding incurs substantial redundancy when addressing inherently localized bugs. In this work, we challenge this inefficient paradigm and propose DiffPDE, a framework leveraging discrete diffusion language models for targeted code repair. By introducing a localized re-masking and infilling strategy, DiffPDE regenerates only erroneous regions while preserving correct context, naturally aligning generation with the sparse nature of PDE errors. Furthermore, to handle coupled bugs requiring sequential interventions, we present Iterative Debugging GRPO (ID-GRPO), a reinforcement learning scheme that enables multi-round debugging within single trajectories via intermediate rewards. Experiments on PDEBench show that DiffPDE achieves competitive accuracy, outperforms same-scale AR models, and significantly accelerates repair.
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