Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models

Abstract: The success of diffusion models has driven interest in performing conditional sampling via training-free guidance of the denoising process to solve image restoration and other inverse problems. A popular class of methods, based on Diffusion Posterior Sampling (DPS), attempts to approximate the intractable posterior score function directly. In this work, we present a novel expression for the exact posterior score for purely denoising tasks that is tractable in terms of the unconditional score function. We leverage this result to analyze the time-dependent error in the DPS score for denoising tasks and compute step sizes on the fly to minimize the error at each time step. We demonstrate that these step sizes are transferable to related inverse problems such as colorization, random inpainting, and super resolution. Despite its simplicity, this approach is competitive with state-of-the-art techniques and enables sampling with fewer time steps than DPS.