ABSTRACT Accreting neutron stars and black holes in low-mass X-ray binaries (LMXBs) radiate across the electromagnetic spectrum. Linking the emission produced at different wavelengths can provide valuable information about the accretion process and any associated outflows. In this work, we study simultaneous X-ray and ultraviolet (UV)/optical observations of the neutron star LMXB Aql X-1, obtained with the Neil Gehrels Swift Observatory during its 2013, 2014, and 2016 accretion outbursts. We find that the UV/optical and X-ray emission are strongly correlated during all three outbursts. For the 2013 and 2014 episodes, which had the best Swift sampling, we find that the correlation between the UV/optical and X-ray fluxes is significantly steeper during the decay (soft state) of the outburst than during the rise (hard-to-soft state). We observe a UV/optical hysteresis behaviour that is likely linked to the commonly known X-ray spectral hysteresis pattern. For the decays of the three outbursts, we obtain a correlation index that cannot be directly explained by any single model. We suspect that this is a result of multiple emission processes contributing to the UV/optical emission, but we discuss alternative explanations. Based on these correlations, we discuss which mechanisms are likely dominating the UV/optical emission of Aql X-1.