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The "Height Variation Hypothesis" is an indirect approach used to estimate forest biodiversity through remote sensing data, stating that greater tree height heterogeneity (HH) measured by CHM LiDAR data indicates higher forest structure complexity and tree species diversity. This approach has traditionally been analyzed using only airborne LiDAR data, which limits its application to the availability of the dedicated flight campaigns. In this study we analyzed the relationship between tree species diversity and HH, calculated with four different heterogeneity indices using two freely available CHMs derived from the new space-borne GEDI LiDAR data. The first, with a spatial resolution of 30 m, was produced through a regression tree machine learning algorithm integrating GEDI LiDAR data and Landsat optical information. The second, with a spatial resolution of 10 m, was created using Sentinel-2 images and a deep learning convolutional neural network. We tested this approach separately in 30 forest plots situated in the northern Italian Alps, in 100 plots in the forested area of Traunstein (Germany) and successively in all the 130 plots through a cross-validation analysis. Forest density information was also included as influencing factor in a multiple regression analysis. Our results show that the GEDI CHMs can be used to assess biodiversity patterns in forest ecosystems through the estimation of the HH that is correlated to the tree species diversity. However, the results also indicate that this method is influenced by different factors including the GEDI CHMs dataset of choice and their related spatial resolution, the heterogeneity indices used to calculate the HH and the forest density. Our finding suggest that GEDI LIDAR data can be a valuable tool in the estimation of forest tree heterogeneity and related tree species diversity in forest ecosystems, which can aid in global biodiversity estimation., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors.)