VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models

Edward Li, Zichen Wang, Jiahe Huang, Jeong Joon Park

Keywords: Partial differential equations, Video diffusion models, Sparse observation, Data Imputation, Uncertainty Quantification

TL;DR: We present a unified framework for predicting forward/inverse/partial PDE soltuions under ambiguity using a video inpainting diffusion model.

Abstract: We introduce a unified generative framework for solving partial differential equations (PDEs) and quantifying predictive uncertainty across forward, inverse, and partial-observation tasks. In contrast to prior approaches that design separate strategies for each setting, we recast PDE solving as a generalized video inpainting problem, where future or missing spatiotemporal states are inferred from arbitrary patterns of observed data. Our method employs a pixel-space transformer diffusion model that directly operates on physical fields, avoiding the accuracy degradation observed with latent-space representations in scientific domains. To enhance efficiency, we incorporate a hierarchical transformer strategy that balances resolution, fidelity, and computational cost. This design enables fine-grained, high-quality reconstructions together with per-pixel uncertainty estimates that capture spatial and temporal variability. Extensive experiments on five representative synthetic PDE benchmarks and a real-world ERA5 dataset demonstrate that our framework consistently outperforms state-of-the-art baselines, offering a versatile and robust approach to scientific and engineering applications.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 14656