DiffPDE: Masked Diffusion Language Models as PDE Solver

2026-08-31

AI Summary

本文提出DiffPDE，一种基于离散扩散语言模型的方法，通过局部重新掩码和填充策略修复偏微分方程求解器中的错误，并结合迭代调试GRPO提高效率。

Abstract

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.

Problem

• Partial Differential Equation
• autoregressive models
• localized bugs
• redundancy

Innovation

• Diffusion Language Models
• Localized Re-masking and Infilling
• Iterative Debugging GRPO