VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models

• URL: http://arxiv.org/abs/2506.13754v2
• Date: Tue, 17 Jun 2025 02:15:17 GMT
• Title: VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models
• Authors: Edward Li, Zichen Wang, Jiahe Huang, Jeong Joon Park,
• Abstract summary: We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models.<n>Our method proposes pixel-space video diffusion models for fine-grained, high-fidelity inpainting and conditioning.<n>Our method offers an accurate and versatile solution across a wide range of PDEs and problem setups, outperforming state-of-the-art baselines.
• Score: 8.189440319895823
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under full or partial observation, our approach unifies these tasks under a single, flexible generative framework. Specifically, we recast PDE-solving as a generalized inpainting problem, e.g., treating forward prediction as inferring missing spatiotemporal information of future states from initial conditions. To this end, we design a transformer-based architecture that conditions on arbitrary patterns of known data to infer missing values across time and space. Our method proposes pixel-space video diffusion models for fine-grained, high-fidelity inpainting and conditioning, while enhancing computational efficiency through hierarchical modeling. Extensive experiments show that our video inpainting-based diffusion model offers an accurate and versatile solution across a wide range of PDEs and problem setups, outperforming state-of-the-art baselines.

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