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DiffPDE introduces a discrete diffusion language model framework that optimizes code repair for Partial Differential Equation solvers by focusing regeneration on localized errors rather than using inefficient global autoregressive decoding. The approach further employs an iterative reinforcement learning scheme to handle coupled bugs, demonstrating superior accuracy and speed over standard models in experimental benchmarks. This work represents a significant methodological shift in applying generative AI techniques to specialized scientific computing tasks.
DiffPDE: Masked Diffusion Language Models as PDE Solver
arXiv:2608.30532v1 Announce Type: new 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.
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.
Artificial Intelligence (cs.AI)
arXiv:2608.30532 [cs.AI]
(or arXiv:2608.30532v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2608.30532 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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