Diffusion-Based Posterior Sampling: A Feynman-Kac Analysis of Bias and Stability
This research analyzes bias and stability in diffusion-based posterior samplers used for inverse problems. The authors introduce a surrogate path to characterize where samplers over- or under-sample by linking it to a parabolic PDE. They show that early guidance stopping acts as a weighted prior, providing a mechanism to reduce numerical instabilities and oscillations in the sampling process.