Diffusion-Based Inverse Problems

These methods reconstruct hidden images or physical fields from measurements such as sparse MRI data, blurred images, or limited-angle CT projections, where many solutions may fit the observations. A pretrained diffusion model supplies a prior over plausible solutions, combined with measurement guidance through posterior sampling, plug-and-play optimization, or physics-informed conditioning. Current work also explores latent-space and distilled models to reduce inference costs, while using ensembles or sampling to estimate uncertainty. A central challenge is balancing measurement fidelity with realistic detail without hallucinating unsupported content, especially under model mismatch or distribution shift, while making posterior estimates reliable and computation practical.