mlsanityData to 7 Oct 2026

DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solving

arXiv 2602.13616 ↗First posted 14 Feb 2026cs.AI cs.LGcited by 4

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

We propose DiffusionRollout, a novel selective rollout planning strategy for autoregressive diffusion models, aimed at mitigating error accumulation in long-horizon predictions of physical systems governed by partial differential equations (PDEs). Building on the recently validated probabilistic approach to PDE solving, we further explore its ability to quantify predictive uncertainty and demonstrate a strong correlation between prediction errors and standard deviations computed over multiple samples-supporting their use as a proxy for the model's predictive confidence. Based on this observation, we introduce a mechanism that adaptively selects step sizes during autoregressive rollouts, improving long-term prediction reliability by reducing the compounding effect of conditioning on inaccurate prior outputs. Extensive evaluation on long-trajectory PDE prediction benchmarks validates the effectiveness of the proposed uncertainty measure and adaptive planning strategy, as evidenced by lower prediction errors and longer predicted trajectories that retain a high correlation with their ground truths.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 46 of its 55 references that are in the map. First posted on arXiv 14 Feb 2026.

Builds on

46 of 55 references.

Closest ancestors · 4

Same direction, newest first

  1. 2024Wavelet Diffusion Neural Operator6 Dec
  2. 2024On conditional diffusion models for PDE simulations21 Oct
  3. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observation25 Jun
  4. 2024Rolling Diffusion Models12 Feb

Other references · 42

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Denoising Diffusion Implicit Modelscited by 9,655
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2022Scalable Diffusion Models with Transformerscited by 5,931
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  7. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  8. 2020Reformer: The Efficient Transformercited by 1,658
  9. 2020Rethinking Attention with Performerscited by 1,584
  10. 2024Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Predictioncited by 1,005
  11. 2015Scheduled Sampling for Sequence Prediction with Recurrent Neural Networkscited by 779
  12. 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
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  4. 2015Sequence Level Training with Recurrent Neural Networkscited by 568
  5. 2019Neural Text Generation with Unlikelihood Trainingcited by 489
  6. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  7. 2021Choose a Transformer: Fourier or Galerkincited by 333
  8. 2023GNOT: A General Neural Operator Transformer for Operator Learningcited by 321
  9. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  10. 2024Infinity: Scaling Bitwise AutoRegressive Modeling for High-Resolution Image Synthesiscited by 297
  11. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  12. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  13. 2022FourCastNet: Accelerating Global High-Resolution Weather Forecasting using Adaptive Fourier Neural Operatorscited by 188
  14. 2025History-Guided Video Diffusioncited by 165
  15. 2016An Actor-Critic Algorithm for Sequence Predictioncited by 158
  16. 2024The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learningcited by 134
  17. 2019Bridging the Gap between Training and Inference for Neural Machine Translationcited by 123
  18. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  19. 2022Why Exposure Bias Matters: An Imitation Learning Perspective of Error Accumulation in Language Generationcited by 106
  20. 2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
  21. 2024Latent Neural Operator for Solving Forward and Inverse PDE Problemscited by 76
  22. 2023Improved Operator Learning by Orthogonal Attentioncited by 58
  23. 2019Reinforcement Learning Based Graph-to-Sequence Model for Natural Question Generationcited by 57
  24. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 52
  25. 2024APEBench: A Benchmark for Autoregressive Neural Emulators of PDEscited by 51
  26. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 35
  27. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 25
  28. 2024Shedding Light on Large Generative Networks: Estimating Epistemic Uncertainty in Diffusion Modelscited by 22
  29. 2017SEARNN: Training RNNs with Global-Local Lossescited by 17
  30. 2019Rethinking Exposure Bias In Language Modelingcited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulationcited by 4
  2. 2026On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancementcited by 0
  3. 2026Round-Trip Consistency: Bidirectional Diffusion Models Can Predict Their Own Rollout Errorscited by 0
  4. 2026Staying on the Attractor: Supervising Neural Surrogates of 3D Turbulence Where They Leave Itcited by 0

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  1. 2026Bias-Constrained Diffusion Schedules for PDE Emulations: Reconstruction Error Minimization and Efficient Unrolled Training
  2. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation
  3. 2026PDE-regularized Dynamics-informed Diffusion with Uncertainty-aware Filtering for Long-Horizon Dynamics
  4. 2026Memory-Conditioned Flow-Matching for Stable Autoregressive PDE Rollouts
  5. 2023PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
  6. 2025Elucidated Rolling Diffusion Models for Probabilistic Forecasting of Complex Dynamics
  7. 2025Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow prediction
  8. 2026Autoregression-Free Neural Operators for Time-Dependent PDEs