Physics-Informed Generative Modeling

The field develops models that generate distributions of physical fields, trajectories, images, and structures while respecting equations, conservation laws, geometry, or sensor physics. Common approaches include diffusion and flow matching with PDE-residual losses, constraint-preserving projections or manifold parameterizations, differentiable simulators, and physics-guided inference. Applications range from PDE inverse problems and uncertainty estimation to weather forecasting, medical imaging, materials design, molecular modeling, and physically plausible video. A central challenge is balancing physical validity with fidelity to the data distribution: stronger constraints can introduce bias or reduce diversity, while uncertainty calibration, out-of-distribution performance, and sampling cost remain important tests.