Physics-Informed Diffusion Models

This field studies how to make diffusion models generate or recover data that obey physical laws, especially when observations are sparse, noisy, or incomplete. Common approaches add PDE residuals, conservation laws, or boundary conditions to training, or enforce constraints during sampling with differentiable solvers, projections, and measurement guidance. Applications include scientific field generation and forecasting, inverse problems such as imaging and seismic reconstruction, and physically plausible motion. A central tension is improving physical consistency without distorting the data distribution, while keeping inference efficient and uncertainty reliable.