核心概念
Efficiently sample from posterior using DCPS for denoising diffusion priors.
要約
The article discusses the challenges of sampling from the posterior distribution of Denoising Diffusion Models (DDM) as priors for solving Bayesian inverse problems. It introduces the Divide-and-Conquer Posterior Sampler (DCPS) as a powerful sampling scheme that targets a sequence of distributions forming a smooth path between Gaussian distribution and the given posterior. The algorithm utilizes intermediate distributions and simpler posterior sampling problems to reduce approximation errors compared to previous methods. Empirical demonstrations show high reconstruction capability on synthetic data and various restoration tasks.
統計
"Many current challenges in machine learning can be encompassed into linear inverse problems, such as superresolution, deblurring, and inpainting."
"To tackle this issue, we consider in this paper a Bayesian framework which involves the specification of the conditional distribution of the observation y given x—referred to as the likelihood—and the prior distribution of x."
"In this work, we propose the DIVIDE-AND-CONQUER POSTERIOR SAMPLER (DCPS) for denoising diffusion priors, a powerful sampling scheme for Bayesian inverse problems."
"We illustrate the benefits of our methodology and its high reconstruction capability on synthetic data and various restoration tasks."
引用
"We propose the DIVIDE-AND-CONQUER POSTERIOR SAMPLER (DCPS) for denoising diffusion priors."
"Our aim is now to define a sequence of distributions guiding the sampler towards the target posterior py0 = pyk0."
"The results are given in Table 1."