Provable diffusion-based posterior sampling for linear inverse problems via DDIM

TL;DR - PDDIM is an efficient DDIM-based posterior sampler for noisy linear inverse problems that makes coordinate-wise updates informed by the measurement operator. It offers provable convergence to the Bayesian posterior and strong image-restoration performance.

• Samples independently along the measurement operator’s singular directions.
• Switches between the learned diffusion prior and a calibrated measurement predictor based on relative SNR.
• Requires only lightweight modifications to standard DDIM updates.
• Outperforms existing diffusion posterior samplers on most evaluated image-restoration metrics.