The recent development of soft fluidic analogs to electrical components aims to reduce the demand for rigid and bulky electromechanical valves and hard electronic controllers within soft robots. This ongoing effort is advanced in this work by creating sheet‐based fluidic diodes constructed from readily available flexible sheets of polymers and textiles using a layered fabrication approach amenable to manufacturing at scale. These sheet‐based fluidic diodes restrict reverse flow over a wide range of differential pressures—exhibiting a diodicity (the ratio of resistance to reverse vs forward flow) of approximately 100×—to address functional limitations exhibited by prior soft fluidic diodes. By harnessing the diode's highly unidirectional flow, soft devices capable of 1) facilitating the capture and storage of pressurized fluid, 2) performing Boolean operations using diode logic, 3) enabling binary encoding of circuits by preventing interactions between different pressurized input lines, and 4) converting oscillating input pressures to a direct current‐like, positively phased output are realized. This work exemplifies the use of fluidic diodes to achieve complex patterns of actuation and unique capabilities through embedded fluidic circuitry, enabling future development of sheet‐based systems—including wearable and assistive robots made from textiles—as well as other soft robotic devices.