@inproceedings{guo-etal-2026-diffpde,
title = "{D}iff{PDE}: Masked Diffusion Language Models as {PDE} Solver",
author = "Guo, Wenxuan and
Hong, Yuyang and
Fan, Lubin and
Fu, Zhaojin and
Chen, Lin and
Ding, Kun and
Xiang, Shiming",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.57/",
pages = "1169--1186",
ISBN = "979-8-89176-462-0",
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."
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<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>
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%0 Conference Proceedings
%T DiffPDE: Masked Diffusion Language Models as PDE Solver
%A Guo, Wenxuan
%A Hong, Yuyang
%A Fan, Lubin
%A Fu, Zhaojin
%A Chen, Lin
%A Ding, Kun
%A Xiang, Shiming
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F guo-etal-2026-diffpde
%X 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.
%U https://aclanthology.org/2026.findings-emnlp.57/
%P 1169-1186
Markdown (Informal)
[DiffPDE: Masked Diffusion Language Models as PDE Solver](https://aclanthology.org/2026.findings-emnlp.57/) (Guo et al., Findings 2026)
ACL
- Wenxuan Guo, Yuyang Hong, Lubin Fan, Zhaojin Fu, Lin Chen, Kun Ding, and Shiming Xiang. 2026. DiffPDE: Masked Diffusion Language Models as PDE Solver. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 1169–1186, Budapest, Hungary. Association for Computational Linguistics.