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Face anti-spoofing (FAS) plays a vital role in face recognition systems. Most state-of-the-art FAS methods 1) rely on stacked convolutions and expert-designed network, which is weak in describing detailed fine-grained information and easily being ineffective when the environment varies (e.g., different illumination), and 2) prefer to use long sequence as input to extract dynamic features, making them difficult to deploy into scenarios which need quick response. Here we propose a novel frame level FAS method based on Central Difference Convolution (CDC), which is able to capture intrinsic detailed patterns via aggregating both intensity and gradient information. A network built with CDC, called the Central Difference Convolutional Network (CDCN), is able to provide more robust modeling capacity than its counterpart built with vanilla convolution. Furthermore, over a specifically designed CDC search space, Neural Architecture Search (NAS) is utilized to discover a more powerful network structure (CDCN++), which can be assembled with Multiscale Attention Fusion Module (MAFM) for further boosting performance. Comprehensive experiments are performed on six benchmark datasets to show that 1) the proposed method not only achieves superior performance on intra-dataset testing (especially 0.2% ACER in Protocol-1 of OULU-NPU dataset), 2) it also generalizes well on cross-dataset testing (particularly 6.5% HTER from CASIA-MFSD to Replay-Attack datasets). The codes are available at \href{https://github.com/ZitongYu/CDCN}{https://github.com/ZitongYu/CDCN}.