This paper proposes using topology optimization to design fixed-geometry fluid diodes that allow easy passage of fluid flowing in one direction while inhibiting flow in the reverse direction. Fixed-geometry diodes do not use movable mechanical parts or deformations, but rather utilize inertial forces of the fluid to achieve this flow behavior. Diode performance is measured by diodicity, defined as the ratio of pressure drop of reverse flow and forward flow, or equivalently the ratio of dissipation of reverse and forward flow. Diodicity can then be maximized by minimizing forward dissipation while maximizing reverse dissipation. While significant research has been conducted in topology optimization of fluids for minimizing dissipation, maximizing dissipation introduces challenges in the form of small, mesh dependent flow channels and that artificial flow in solid region becomes (numerically) desirable. These challenges are circumvented herein using projection methods for controlling the minimum length scale of channels and by introducing an additional penalty term on flow through intermediate porosities. Several solutions are presented, one of which is fabricated by 3D printing and experimentally tested to demonstrate the diodelike behavior.