  Nonreciprocity in superconductors is attracting much interest owing to its
fundamental importance as well as its potential applicability to engineering.
In this paper, we generalize the previous theories of the intrinsic
superconducting diode effect (SDE) and microscopically elucidate its
relationship with the nonreciprocity of the transition lines under
supercurrent. We derive a general formula for the intrinsic SDE by using the
phenomenological Ginzburg-Landau theory and thereby show that the SDE is
determined by the relative angle between the magnetic field and an effective
anti-symmetric spin-orbit coupling defined from the Ginzburg-Landau
coefficients. The obtained formula offers a convenient criterion to obtain a
finite SDE. We also study the SDE and the nonreciprocal phase transitions of
the $s$-wave and $d$-wave superconductors by using the mean-field theory. It is
established that the sign reversal of the SDE accompanied by the crossover of
the helical superconductivity is a general feature irrespective of the system
details. We study the phase transition lines in the temperature-magnetic-field
phase diagram under the supercurrent, and clarify that the sign reversal of the
SDE generally accompanies the crossings of the transition lines under positive
and negative current directions. Furthermore, the superconducting phases under
the supercurrent even become re-entrant under moderate strength of the electric
current, implying the current-induced first-order phase transitions. Our
findings establish the electric current as the control parameter and the
powerful probe to study the superconducting properties related to the
finite-momentum Cooper pairs.
