On Diffusion Posterior Sampling

This talk examines how pre-trained score networks can be leveraged to efficiently sample from a prior distribution. Specifically, we focus on using these models to sample from a "tilted" prior—the posterior—by creating a vector field that pushes the sampling dynamics directly toward the target distribution . We will center our discussion on Diffusion Posterior Sampling (DPS), a widely adopted algorithm for this exact problem. However, despite its popularity, it is known to fail for simple Gaussian cases. In this talk, by using a Feynman-Kac we will reveal what is the measure that the algorithm is actually sampling from. Our analysis will show that this algorithm is prone to mode collapse, by effectively changing the temperature of the tilt. We will show how our analysis also applies to a wide family of competing algorithms.