用视频修复模型统一求解各类偏微分方程，一次训练通吃正反问题。
VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models
- 将方程求解转化为时空缺失信息的修复任务，用Transformer建模任意观测条件下的推理。
- 在10+类典型偏微分方程上实现高精度预测，对完整与部分观测均有效。
- 适合需要通用、高保真物理模拟的科研与工程场景，尤其适用于逆问题求解。
我们提出一种基于视频修复扩散变换器模型的统一偏微分方程（PDE）求解框架。与现有方法针对正问题或逆问题、全观测或部分观测设计专用策略不同，本方法将所有任务统一为一个灵活的生成式框架。具体而言，将PDE求解重构为广义的图像修复问题：例如，正向预测即从初始条件推断未来状态的缺失时空信息。为此，我们设计了基于Transformer的架构，可对任意已知数据模式进行条件建模，以推断时空维度上的缺失值。方法采用像素空间的视频扩散模型实现细粒度、高保真修复与条件控制，并通过分层建模提升计算效率。大量实验表明，该视频修复式扩散模型在多种典型偏微分方程及问题设置下均表现优异，显著优于当前最优基线。
原文摘要 · Abstract (English)
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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