Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solvers

• URL: http://arxiv.org/abs/2403.12063v2
• Date: Sat, 1 Jun 2024 10:54:50 GMT
• Title: Consistency Model is an Effective Posterior Sample Approximation for Diffusion Inverse Solvers
• Authors: Tongda Xu, Ziran Zhu, Jian Li, Dailan He, Yuanyuan Wang, Ming Sun, Ling Li, Hongwei Qin, Yan Wang, Jingjing Liu, Ya-Qin Zhang,
• Abstract summary: Previous approximations rely on the posterior means, which may not lie in the support of the image distribution. We introduce a novel approach for posterior approximation that guarantees to generate valid samples within the support of the image distribution.
• Score: 28.678613691787096
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion Inverse Solvers (DIS) are designed to sample from the conditional distribution $p_{\theta}(X_0|y)$, with a predefined diffusion model $p_{\theta}(X_0)$, an operator $f(\cdot)$, and a measurement $y=f(x'_0)$ derived from an unknown image $x'_0$. Existing DIS estimate the conditional score function by evaluating $f(\cdot)$ with an approximated posterior sample drawn from $p_{\theta}(X_0|X_t)$. However, most prior approximations rely on the posterior means, which may not lie in the support of the image distribution, thereby potentially diverge from the appearance of genuine images. Such out-of-support samples may significantly degrade the performance of the operator $f(\cdot)$, particularly when it is a neural network. In this paper, we introduces a novel approach for posterior approximation that guarantees to generate valid samples within the support of the image distribution, and also enhances the compatibility with neural network-based operators $f(\cdot)$. We first demonstrate that the solution of the Probability Flow Ordinary Differential Equation (PF-ODE) with an initial value $x_t$ yields an effective posterior sample $p_{\theta}(X_0|X_t=x_t)$. Based on this observation, we adopt the Consistency Model (CM), which is distilled from PF-ODE, for posterior sampling. Furthermore, we design a novel family of DIS using only CM. Through extensive experiments, we show that our proposed method for posterior sample approximation substantially enhance the effectiveness of DIS for neural network operators $f(\cdot)$ (e.g., in semantic segmentation). Additionally, our experiments demonstrate the effectiveness of the new CM-based inversion techniques. The source code is provided in the supplementary material.

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