VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models

Edward Li*, Zichen Wang*, Jiahe Huang*, Jeong Joon Park
University of Michigan, Ann Arbor
*Denotes Equal Contribution
Paper Code (Coming soon) 🤗 Dataset

Additional Video Results

Wave-Layer Continuous 1% observations

Input
DiffusionPDE (Ext.)
Shu et al.
Zhuang et al.
Ours
GT

Wave-Layer Forward

First image
Input (First Frame)
DeepONet
FNO
PINO
Ours
GT

Wave-Layer Inverse

First image
Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

Wave-Layer Inverse 3% observation

First image
Input (Last Frame)
PINO (Interpolated)
Ours
GT

Navier–Stokes Continuous 1% observations

Input
DiffusionPDE (Ext.)
Shu et al.
Zhuang et al.
Ours
GT

Navier–Stokes Forward

First image
Input (First Frame)
DeepONet
FNO
PINO
Ours
GT

Navier–Stokes Inverse

First image
Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

Kolmogorov Flow Forward

First image
Input (First Frame)
DeepONet
FNO
PINO
Ours
GT

Kolmogorov Flow Inverse

First image
Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

Kolmogorov Flow Autoregress 100 Frames

First image
Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

Kolmogorov Flow Autoregress 3% Observation 100 Frames

First image
Input (First Frame)
PINO (Interpolated)
Ours
GT

Kolmogorov Flow Continuous 3% observations 100 Frames

Input
DiffusionPDE (Ext.)
Shu et al.
Zhuang et al.
Ours
GT

Kolmogorov Flow Continuous 1% observations 100 Frames

Input
PINO
Ours
GT

Allen–Cahn Forward

First image
Input (First Frame)
PINO
Ours
GT

Allen–Cahn Inverse

First image
Input (Last Frame)
PINO
Ours
GT

BibTeX

@article{li2025videopde,
    author    = {Edward Li and Zichen Wang and Jiahe Huang and Jeong Joon Park},
    title     = {VideoPDE: Unified Generative PDE Solving via Video},
    journal   = {arXiV},
    year      = {2025},
}