Exploiting the Exact Denoising Posterior Score in Training-Free Guidance of Diffusion Models
This work addresses the challenge of improving training-free guidance for diffusion models in image processing tasks, offering an incremental advancement over existing techniques.
The paper tackles the problem of conditional sampling in diffusion models for image restoration and inverse problems by deriving an exact expression for the posterior score in denoising tasks, which is used to analyze errors in existing methods and compute adaptive step sizes. The result is a competitive approach that enables sampling with fewer time steps than prior methods like Diffusion Posterior Sampling (DPS).
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.