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ARXIV:2604.09058 · DYNAMICS PREDICTION · SUBMITTED 13 APR · 20:28 UTC · FRESHNESS STALE
ARXIV:2604.09058DYNAMICS PREDICTIONSUBMITTED 13 APR · 20:28 UTCFRESHNESS STALEMin Young Baeg · Yoon-Yeong Kim · arXiv
A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering.
Opportunity summary
Pain A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering.
Evidence 0 refs | 3 sources | 50% coverage
Blocker Evidence unverified
A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squared error objectives…
Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches…
ScienceToStartup currently rates this 3.0/10 on the public viability pass. Extensive experiments on multiple dynamical datasets demonstrate that PDYffusion achieves superior performance in terms of CRPS and MSE, while maintaining stable uncertainty behavior measured…
Dynamics Prediction moved forward this cycle; last verified April 2026. Public score 3.0/10. Production flags indicate code availability.
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A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering.
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10.48550/arXiv.2604.09058A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering.
Abstract
Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squared error objectives and fail to capture the underlying dynamics governed by physical laws. In this work, we propose PDYffusion, a dynamics-informed diffusion framework that integrates PDE-based regularization and uncertainty-aware forecasting for stable long-term prediction. The proposed method consists of two key components: a PDE-regularized interpolator and a UKF-based forecaster. The interpolator incorporates a differential operator to enforce physically consistent intermediate states, while the forecaster leverages the Unscented Kalman Filter to explicitly model uncertainty and mitigate error accumulation during iterative prediction. We provide theoretical analyses showing that the proposed interpolator satisfies PDE-constrained smoothness properties, and that the forecaster converges under the proposed loss formulation. Extensive experiments on multiple dynamical datasets demonstrate that PDYffusion achieves superior performance in terms of CRPS and MSE, while maintaining stable uncertainty behavior measured by SSR. We further analyze the inherent trade-off between prediction accuracy and uncertainty, showing that our method provides a balanced and robust solution for long-horizon forecasting.
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PROBLEM
A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squar...
METHOD
Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches...
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. Extensive experiments on multiple dynamical datasets demonstrate that PDYffusion achieves superior performance in terms of CRPS and MSE, while maintaining stable uncertainty behavior measured by SSR. Code...
WHY NOW
Dynamics Prediction moved forward this cycle; last verified April 2026. Public score 3.0/10. Production flags indicate code availability.
Abstract-backed public claims while anchored extraction refreshes.
A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squared error objectives and fail to capture the underlying dynamics governed by physical laws.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for modeling uncertainty, conventional approaches often rely on mean squared error objectives and fail to capture the underlying dynamics governed by physical laws.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. Extensive experiments on multiple dynamical datasets demonstrate that PDYffusion achieves superior performance in terms of CRPS and MSE, while maintaining stable uncertainty behavior measured by SSR. Code availability is flagged in the production record; the public repository link still needs proof alignment.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Dynamics Prediction moved forward this cycle; last verified April 2026. Public score 3.0/10. Production flags indicate code availability.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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A dynamics-informed diffusion framework for stable long-horizon spatiotemporal prediction using PDE regularization and uncertainty-aware filtering.
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