Title: Faster Neural Architecture "Search" for Deep Image Prior. Abstract: Deep image prior (DIP) is known for leveraging the spectral bias of the convolutional neural network (CNN) towards lower frequencies in various single-image restoration tasks.  Such inductive bias has been widely attributed to the network architecture. Existing studies therefore either handcraft the architecture or use automated neural architecture search (NAS). However, there is still a lack of understanding on how the architectural choice corresponds to the image to be restored, leading to an excessively large search space that is both time and computationally-expensive for typical NAS techniques. As a result, the architecture is often searched and fixed for the whole dataset, while the best-performing one could be image-dependent. Moreover, common architecture search requires ground truth supervision, which is often not accessible. In this work, we present a simple yet effective \emph{training-free} approach to estimate the required architecture for \emph{every image} in advance. This is motivated by our empirical findings that the width and depth of a good network prior are correlated with the texture of the image, which can be estimated during pre-processings. Accordingly, the design space is substantially shrunk to a handful of subnetworks within a given large network. The experiments on denoising across different noise levels show that a subnetwork with proper setups could be a more effective network prior than the original network while being highly under-parameterized, making it not critically require early-stopping as with the original large network.