The emergence of Neolithic economies and their spread through Eurasia was one of the most crucial transitions of the Holocene, with different mechanisms of diffusion-demic, cultural-being proposed. While this phenomenon has been exhaustively studied in Europe, with repeated attempts to model the speed of Neolithic diffusion based on radiocarbon dates, much less attention has been devoted to the dispersal towards the East, and in particular to South Asia. The Neolithic in the latter region at least partly derived from southwest Asia, given the presence of "founder crops" such as wheat and barley. The process of their eastward diffusion, however, may have been significantly different to the westward dispersal, which was mainly due to demic diffusion, as local domesticates were already available and farming was already practiced in parts of South Asia. Here, we use radiocarbon dates specifically related to the spread of the southwest Asian Neolithic crops to model the speed of dispersal of this agricultural package towards South Asia. To assess potential geographical and environmental effects on the dispersal, we simulate different speeds depending on the biomes being crossed, employing a genetic algorithm to search for the values that most closely approach the radiocarbon dates. We find that the most important barrier to be crossed were the Zagros mountains, where the speed was lowest, possibly due to topography and climate. A large portion of the study area is dominated by deserts and shrublands, where the speed of advance, albeit closer to the range expected for demic diffusion, was lower than observed in Europe, which can also potentially be attributed to environmental constraints in the adaptation of the crops. Finally, a notable acceleration begins in the Indus valley, exceeding the range of demic diffusion in the tropical and subtropical environments east of the Indus. We propose that the latter is due to the rapid diffusion among populations already familiar with plant cultivation.