Consistency Models Improve Diffusion Inverse Solvers

arXiv:2403.12063v1 Announce Type: cross
Abstract: Diffusion inverse solvers (DIS) aim to find an image $x$ that lives on the diffusion prior while satisfying the constraint $f(x) = y$, given an operator $f(.)$ and measurement $y$. Most non-linear DIS use posterior mean $\hat{x}_{0|t}=\mathbb{E}[x_0|x_t]$ to evaluate $f(.)$ and minimize the distance $||f(\hat{x}_{0|t})-y||^2$. Previous works show that posterior mean-based distance is biased; instead, posterior sample $x_{0|t}\sim p_{\theta}(x_0|x_t)$ promises a better candidate. In this paper, we first clarify when is posterior sample better: $1)$ …

abstract aim arxiv cs.cv cs.lg diffusion image linear mean measurement non-linear posterior prior show type