Sutureless, implantable fluid shunting devices and associated methods for controlling the pressure of fluids within anatomical spaces or cavities of the body. The device generally comprises a tube having a diffusion barrier (e.g., diffusion chamber) formed on a proximal end thereof. Fluid which flows through the tube will collect within the diffusion chamber and will diffuse outwardly therethrough. However, the presence of the diffusion chamber will prevent microbes, cells or other matter from interfering with or backflowing through the tube. Additionally, the tube may be provided with a pressure-openable aperture through which fluid from the tube may flow into the diffusion chamber. Such pressure-openable aperture will remain closed, until the pressure of fluid within the tube exceeds a predetermined maximum pressure P.sub.MAX. In this manner, the pressure-openable aperture will limit the amount of fluid drained from the anatomical space or cavity of the body, thereby avoiding hypotony within such anatomical space or cavity. The diffusion barrier of the device is preferably configured to fit between, and to be engaged by, adjacent recti muscles of the eye. Such engagement of the diffusion barrier with the adjacent recti muscles serves to prevent unwanted migration or post-implantation movement of the device, without the need for suturing of the device to the tissue of the eye.