🤖 AI Summary
Diffusion models suffer from low conditional sampling accuracy, large time-dependent errors, and poor sampling efficiency in inverse problems such as image restoration. To address these issues, this paper proposes a training-free Bayesian posterior guidance framework. We first derive an analytical closed-form solution for the posterior score function under pure denoising—replacing conventional approximations—and then design a time-varying adaptive step-size strategy that explicitly minimizes single-step error, with empirical validation of its cross-task generalizability. Our method achieves state-of-the-art performance on denoising, colorization, stochastic inpainting, and super-resolution, while significantly reducing the number of sampling steps compared to DPS—thereby jointly improving both accuracy and efficiency.
📝 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.