Diffusion magnetic resonance imaging (dMRI) tractography is a key technique for reconstructing brain structural connectivity. A widely recognized limitation in tractography is the enforced symmetry of fiber orientation distribution functions (fODFs) in opposite directions, which may impair performance in regions with asymmetric microstructural organization. Previous studies have proposed leveraging anatomical priors or labeled training data to address this limitation; however, such data requirements constrain generalizability. In this study, we propose Recursive-a-fODF, a recursive estimator that uses an unsupervised deep learning framework to directly estimate asymmetric fODFs (a-fODFs) from dMRI data. The model incorporates a recursive calibration process that directly and dynamically estimates the white matter response function from the data itself, eliminating the need for external anatomical priors. We validate the framework using ex vivo marmoset brain data and in vivo human datasets, demonstrating superior performance in resolving complex fiber configurations. When applied to clinical cohorts with neurodegenerative and psychiatric conditions, Recursive-a-fODF reveals disease-specific alterations in fiber orientation asymmetry. These findings demonstrate that a-fODFs, estimated in a purely data-driven manner, can capture microstructural signatures relevant to disease pathology. Collectively, this work establishes a-fODF-based modeling as a powerful, anatomically unbiased approach that provides a complementary dimension to conventional diffusion metrics. These technical advances form a foundation for more accurate tractography and offer a new avenue for developing sensitive neuroimaging biomarkers.