# VideoPDE: Unified Generative PDE Solving via Video Inpainting Diffusion Models

## Additional Video Results

## Wave-Layer Continuous 1% observations

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

## Wave-Layer Forward

Input (First Frame)
DeepONet
FNO
PINO
Ours
GT

## Wave-Layer Inverse

Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

## Wave-Layer Inverse 3% observation

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

Input (First Frame)
DeepONet
FNO
PINO
Ours
GT

## Navier–Stokes Inverse

Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

## Kolmogorov Flow Forward

Input (First Frame)
DeepONet
FNO
PINO
Ours
GT

## Kolmogorov Flow Inverse

Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

## Kolmogorov Flow Autoregress 100 Frames

Input (Last Frame)
DeepONet
FNO
PINO
Ours
GT

## Kolmogorov Flow Autoregress 3% Observation 100 Frames

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

Input (First Frame)
PINO
Ours
GT

### Allen–Cahn Inverse

Input (Last Frame)
PINO
Ours
GT

### ERA5 3% Continuous

Input
Ours
GT

### ERA5 10% Continuous

Input
Ours
GT