Technology Category
Computer Vision: Diffusion Models for VisionKnowledge Representation and Reasoning: Geometric, Spatial, and Temporal ReasoningMachine Learning: Deep Neural Architectures and Foundation Models
VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models
🤖 AI Summary
This work addresses the unified solution of both forward and inverse partial differential equation (PDE) problems—under fully observed or partially observed (incomplete) conditions. The method reformulates PDE solving as a spatiotemporal video inpainting task, leveraging a pixel-level video diffusion model enhanced with spatiotemporal masking conditioning and hierarchical conditional modeling to generate high-fidelity spatiotemporal solutions from initial/boundary/sparse observations. It is the first framework to enable end-to-end unified modeling across forward/inverse and complete/incomplete-observation PDE scenarios. Technically, it introduces a video diffusion Transformer architecture coupled with hierarchical computational optimization strategies. Evaluated on diverse PDE families—including reaction-diffusion, Navier–Stokes, and wave equations—the approach achieves significant improvements over state-of-the-art methods in accuracy, generalization across unseen PDEs and domains, and inference efficiency.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Unified framework for solving PDEs using video-inpainting diffusion models
Recasts PDE-solving as generalized spatiotemporal inpainting problem
Enhances accuracy and efficiency across diverse PDE problem setups
Innovation
Methods, ideas, or system contributions that make the work stand out.
Unified PDE solving via video-inpainting diffusion models
Transformer-based architecture for spatiotemporal inference
Hierarchical modeling enhances computational efficiency
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