Turbid river plumes entering ocean or lake water of lesser density (i.e., hyperpycnal plumes) can plunge to form turbidity currents providing an important link between terrestrial sediment sources and marine depositional sinks. A leading hypothesis suggests that hyperpycnal-plume deposits accurately record the rising and falling discharge of a flooding river (in terms of sediment-size grading, bedform sequence, and deposit thickness), which, if correct, has significant implications for unraveling river dynamics, reservoir potential, and Earth history from marine-event beds. Herein, we present one of the first experimental flume studies aimed at testing this hypothesis. Results indicate that depth-averaged hyperpycnal-plume velocities can be uncorrelated or even anti-correlated with river discharge at certain seabed locations because of translation of the plunge point resulting from temporal variations in discharge and sediment concentration through the duration of a river flood. An advection length scale of settling sediment is found to be an important control on hyperpycnal-plume deposits, where coarse sediment (sand) is most likely to record multiple flow accelerations and decelerations related to plunge-point translation even for a river flood with a single-peaked hydrograph. In contrast, fine sediment (mud) is relatively insensitive to local plunge-point dynamics and is most likely to preserve directly rising and falling river discharge. Finally, it was found that the necessary fluvial sediment concentration to form a plunging plume can be much larger than the concentration typically used assuming density equivalence because of deposition upstream of the plunge point.