Abstract We study the recent star formation histories (SFHs) of 575 intermediate-mass galaxies (IMGs, 10⁹ ≤ M/M _⊙ ≤ 10¹⁰) in COSMOS at 0.3 < z < 0.4 by comparing their Hα and UV luminosities. These two measurements trace star formation rates (SFRs) on different timescales and together reveal fluctuations in recent activity. We compute L _Hα from Magellan IMACS spectroscopy, while L _UV is derived from rest-frame 2800 Å photometry. Dust corrections are applied to each band independently. We compare the deviation of L _Hα and L _UV from their respective star-forming sequences (i.e., Δ log L H α and Δ log L UV ), and after accounting for observational uncertainties we find a small intrinsic scatter between the two quantities (σ _δ ≲ 0.03 dex). This crucial observational constraint precludes strong fluctuations in the recent SFHs of IMGs: simple linear SFH models indicate that a population of IMGs would be limited to only factors of ≲2 change in SFR over 200 Myr and ≲30% on shorter timescales of 20 Myr. No single characteristic SFH for IMGs, such as an exponentially rising/falling burst, can reproduce the individual and joint distribution of Δ log L H α and Δ log L UV . Instead, an ensemble of SFHs is preferred. Finally, we find that IMG SFHs predicted by recent hydrodynamic simulations, in which feedback drives rapid and strong SFR fluctuations, are inconsistent with our observations.