There is no much doubt that biotic interactions shape community assembly and ultimately the spatial co-variations between species. There is a hope that the signal of these biotic interactions can be observed and retrieved by investigating the spatial associations between species while accounting for the direct effects of the environment. By definition, biotic interactions can be both symmetric and asymmetric. Yet, most models that attempt to retrieve species associations from co-occurrence or co-abundance data internally assume symmetric relationships between species. Here, we propose and validate a machine-learning framework able to retrieve bidirectional associations by analyzing species community and environmental data. Our framework (1) models pairwise species associations as directed influences from a source to a target species, parameterized with two species-specific latent embeddings: the effect of the source species on the community, and the response of the target species to the community; and (2) jointly fits these associations within a multi-species conditional generative model with different modes of interactions between environmental drivers and biotic associations. Using both simulated and empirical data, we demonstrate the ability of our framework to recover known asymmetric and symmetric associations and highlight the properties of the learned association networks. By comparing our approach to other existing models such as joint species distribution models and probabilistic graphical models, we show its superior capacity at retrieving symmetric and asymmetric interactions. The framework is intuitive, modular and broadly applicable across various taxonomic groups.