  We use gravitational wave (GW) standard sirens, in addition to Type Ia
supernovae (SNIa) and baryon acoustic oscillation (BAO) mock data, to forecast
constraints on the electromagnetic and gravitational distance duality relations
(DDR). We make use of a parameterised approach based on a specific DDR
violation model, along with a machine learning reconstruction method based on
the Genetic Algorithms. We find that GW provide an alternative to the use of
BAO data to constrain violations of the DDR, reaching $3\%$ constraints on the
violation parameter we consider when combined with SNIa, which is only improved
by a factor of $\approx1.4$ if one instead considers the combination of BAO and
SNIa. We also investigate the possibility that a neglected modification of
gravity might lead to a false detection of DDR violations, even when screening
mechanisms are active. We find that such a false detection can be extremely
significant, up to $\approx10\sigma$ for very extreme modified gravity
scenarios, while this reduces to $\approx4\sigma$ in a more realistic case.
False detections can also provide a smoking gun for the modified gravity
mechanism at play, as a result of the tension introduced between the SNIa+GW
and SNIa+BAO combinations.
