Most fluvial and lacustrine landforms on Mars are thought to be old and have formed more than ~3.8 Gyr ago, in the Noachian period. After a major climatic transition, surface liquid water became less abundant and finally disappeared almost completely. Recent work has shown that observational evidence for Hesperian and Amazonian aqueous processes is more common than previously recognized, but their nature is poorly understood. Moreover, it is not clear how the paleoclimate of Mars can be constrained by this activity. Here we report our investigation of a population of deltas around the ancient impact basin Chryse Planitia. To test whether the results are globally applicable, we also studied selected deltas with similar morphologies in the eastern hemisphere and found that the results are consistent. We compared the morphology of deltas, feeder channels, and receiving lakes, dated deltas by crater counting and searched for alteration minerals in hyperspectral images. The valleys and associated late-stage deltas were formed by short-lived aqueous processes, as suggested by their morphology and the general lack of associated aqueous alteration minerals. The likely source of water was neither widespread precipitation nor a regionally connected groundwater aquifer, but water mobilized locally from the cryosphere. Delta formation in our study areas occurred from the Early Hesperian to the Late Amazonian and did not require sustained periods of global climatic conditions favoring widespread precipitation. Liquid surface water has been locally present on Mars even after the Noachian, although only episodically, for transient intervals, and widely separated in space.