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Transport of energy carriers in solid-state materials is determined by their wavefunctions and interactions with the environment. While quantum transport theory has predicted distinct transport in the intermediate coupling regime resulting from the intricate interplay between coherent wave-like and incoherent particle-like mechanisms, these predictions are awaiting experimental evidence. Here we demonstrate quantum transport signatures in perovskite nanocrystal superlattices by imaging exciton propagation with high spatial and temporal resolutions over 7-298 K. At 7 K, coherent propagation of the excitons dominates, with transient ballistic motion within a coherence length of up to 40 nanocrystal sites. The interference of the wave-like motion leads to Anderson Localization in the long-time limit. As temperature increases, a peak in the long-time diffusion constant is observed at a temperature where static disorder and dephasing are balanced, which substantiates evidence for environment-assisted quantum transport. Our results connect theoretical predictions and experiments using a stochastic Anderson localization model, highlighting perovskite nanocrystals as promising building blocks for quantum materials. The interplay between coherent wave-like and incoherent particle-like transport can lead to environment-assisted quantum transport. Using time resolved microscopies and theoretical modeling, the authors show signatures of this enhanced transport regime in perovskite nanocrystal superlattices.