mlsanityData to 14 Oct 2026

DiffPDE: Masked Diffusion Language Models as PDE Solver

arXiv 2608.30532 ↗First posted 31 Aug 2026cs.AIcited by 0

On the map: Diffusion models → Discrete and text diffusion

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Discrete and text diffusion, one of 14 directions in Diffusion models. Builds on 19 of its 34 references that are in the map. First posted on arXiv 31 Aug 2026.

Builds on

19 of 34 references.

Closest ancestors · 1

Same direction, newest first

  1. 2025Dream-Coder 7B: An Open Diffusion Language Model for Code1 Sep

Other references · 18

  1. 2025Qwen3 Technical Reportcited by 8,820
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,719
  4. 2024Qwen2.5-Coder Technical Reportcited by 1,203
  5. 2023Teaching Large Language Models to Self-Debugcited by 988
  6. 2025Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decodingcited by 420
  7. 2021Choose a Transformer: Fourier or Galerkincited by 343
  8. 2025AIDE: AI-Driven Exploration in the Space of Codecited by 226
  9. 2024LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discoverycited by 86
  10. 2025CodePDE: An Inference Framework for LLM-driven PDE Solver Generationcited by 39
  11. 2023Cross-Modal Fine-Tuning: Align then Refinecited by 34
  12. 2024On the Benefits of Memory for Modeling Time-Dependent PDEscited by 31
6 more
  1. 2024UPS: Efficiently Building Foundation Models for PDE Solving via Cross-Modal Adaptationcited by 27
  2. 2025PDE-Controller: LLMs for Autoformalization and Reasoning of PDEscited by 23
  3. 2024Evaluating LLMs' Mathematical and Coding Competency through Ontology-guided Interventionscited by 20
  4. 2025Exploring the Potential of Diffusion Large Language Models in Code Generationcited by 16
  5. 2025FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimizationcited by 11
  6. 2024Component Fourier Neural Operator for Singularly Perturbed Differential Equationscited by 7

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  1. 2025DiffuCoder: Understanding and Improving Masked Diffusion Models for Code Generation
  2. 2026AutoPDE: Reliable Agentic PDE Solving via Explicitly Represented Solver Strategies
  3. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulation
  4. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observation
  5. 2026DiffBench Meets DiffAgent: End-to-End LLM-Driven Diffusion Acceleration Code Generation
  6. 2026Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards
  7. 2025DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning
  8. 2026Diffusion-State Policy Optimization for Masked Diffusion Language Models