## 1 Introduction  
Face super-resolution (FSR), also referred to as face hallucination [1], is a technology that enhances the quality of low-resolution (LR) face images by transforming them into high-resolution (HR) ones. Typically, face images suffer lower spatial resolution due to limited imaging conditions and low-cost imaging equipment. This degradation affects the performance of most practical downstream applications, such as face recognition and face analysis. As a result, FSR has become a popular and essential scientific tool in the fields of computer vision and image processing [2]. Different from general image super-resolution, FSR is a technique that focuses on recovering crucial facial structures. Although these structures only occupy a small portion of the face, they are essential in distinguishing different faces and improving image quality. [PERSON] and [PERSON] [1] proposed the first FSR method, which triggered the upsurge of traditional FSR methods. Afterward, various traditional techniques for FSR have been developed over time, which can mainly resort to the interpolation approach [3], Principal Component Analysis (PCA) [4], convex optimization [5], Bayesian approach [6], kernel regression [7], and manifold learning [8]. Nevertheless, traditional methods are limited in producing plausible facial images due to their shallow structure and representation abilities. Recently, FSR has made significant progress due to the advent of deep learning techniques [2]. Relying on the powerful deep convolution structures, various convolution neural networks (CNNs)-based FSR methods [9, 10, 11, 12, 13] have been developed to predict the fine-grained facial details. However, due to the vanishing gradient problem, the actual receptive field of most CNN-based models is limited. This makes it challenging to model global dependency, resulting in blurry effects in the reconstructed face images. Devoting to capturing both local and global dependencies, transformer-based methods [14; 15] have gained significant attention nowadays. The efficacy of transformer-based methods in improving FSR performance is noteworthy. However, they still exhibit certain limitations that require attention. Transformer-based encoder-decoder networks comprise two major parts: an up/downsample module that connects adjacent-scale feature information and a transformer module that explores and enhances the corresponding-level features. We will discuss the limitations of these components separately below:  
_(1)_ Due to its relatively small network size, the up/downsample module has not received sufficient attention in FSR methods. However, it plays a more important role than the one applied in the general image super-resolution methods. This is because face images are highly structured with eyes, nose, and mouth in a specific location, which is also why some FSR methods require additional marking on the dataset. Nonetheless, as illustrated in Figure 1b, the inner feature maps generated by pixel deconvolutional or shuffle layers have no direct relationship since they are produced by independent convolutional kernels, which can result in significant differences between the values of adjacent pixels. Therefore, an up/downsample module that can build direct relationships among adjacent pixels is in high demand. _(2)_ The transformer module has significantly improved FSR performance. However, raw feature maps are fed to the transformer blocks directly without examining their potential feature information, limiting their performance. As shown in Figure 1g, raw features processed by the transformer block without guiding are not always detail-rich or even buried in gray, which restricts the following transformer blocks to only selecting a limited number of feature maps based on the self-attention heatmap (Figure 1e). On the contrary, applying a guiding block to guide the transformer block about essential facial components results in more correlated feature maps (Figure 1f).