  We identify a new mechanism for the intrinsic superconducting diode effect
(SDE) in multiphase superconductors. Using a Ginzburg-Landau and a microscopic
two-band model, we find phase transitions into a mixed phase with
finite-momentum Cooper pairs and SDE with high (including maximal) diode
efficiencies, despite the individual phases exhibiting no SDE and equal
inversion parity. We thus show that parity mixing $-$ invoked in previous
proposals $-$ is not a crucial ingredient for SDE. The new mechanism may be
relevant in a multitude of known multiphase superconductors like UTe$_2$.
