Water exhibits a variety of anomalous behaviours. To date, many computer simulations and experimental studies have shown compelling evidence for the existence of a liquid–liquid phase transition between the high-density and low-density phases in the deeply supercooled regime and for a critical point that terminates the boundary between the two phases. A possible theoretical scenario concerning the origin of these anomalies is the two-state model of water, which posits that water is composed of two distinct and interconvertible local structures. Here we identify multidimensional reaction coordinates that can provide molecular-level evidence for the generic existence of two local structures undergoing interconvertible reactions in liquid water. By employing unsupervised deep learning on massive molecular dynamics simulations of an accurate and widely used water model, we found that near the high-density/low-density phase boundary, interconvertible reactions proceed via a full-loop reaction pathway with three saddle points, whereas away from it the reactions proceed via a semi-loop pathway with a single saddle point. These findings provide molecular-level evidence in support of the two-state water model and may offer physical insights into the origin of the liquid–liquid phase transitions more generally.