Whole brain tractography is commonly used to study the brain's white matter fiber pathways, but the large number of streamlines generated -up to one million per brain -can be challenging for large-scale population studies. We propose a robust dimensionality reduction framework for tractography, using a Convolutional Variational Autoencoder (ConvVAE) to learn low-dimensional embeddings from white matter bundles. The resulting embeddings can be used to facilitate downstream tasks such as outlier and abnormality detection, and mapping of disease effects on white matter tracts in individuals or groups. We design experiments to evaluate how well embeddings of different dimensions preserve distances from the original high-dimensional dataset, using distance correlation methods. We find that streamline distances and inter-bundle distances are well preserved in the latent space, with a 6-dimensional optimal embedding space. The generative ConvVAE model allows fast inference on new data, and the smooth latent space enables meaningful decodings that can be used for downstream tasks. We demonstrate the use of a ConvVAE model trained on control subjects' data to detect structural anomalies in white matter tracts in patients with Alzheimer's disease (AD). Using ConvVAEs to facilitate population analyses, we identified 6 tracts with statistically significant differences between AD and controls after controlling for age and sex effect, visualizing specific locations along the tracts with high anomalies despite large inter-subject variations in fiber bundle geometry.