Diffractive neural networks (DNNs) have garnered significant attention in recent years as a physical computing framework, combining high computational speed, parallelism, and low-power consumption. However, the non-reconfigurability of cascaded diffraction layers limits the ability of DNNs to perform multitasking, and methods such as replacing diffraction layers or light sources, while theoretically feasible, are difficult to implement in practice. This Letter introduces a flippable diffractive neural network (F-DNN) in which the diffraction layer is an integrated structure processed on both sides of the substrate. This design allows rapid task switching by flipping diffraction layers and overcomes alignment challenges that arise when replacing layers. Classification-based simulation results demonstrate that F-DNN addresses the limitations of traditional multitask DNN architectures, offering both superior performance and scalability, which provides a new approach for realizing high-speed, low-power, and multitask artificial intelligence systems.