Continual learning (CL) with long-tailed data distributions remains a critical challenge for real-world AI systems, where models must sequentially adapt to new classes while retaining knowledge of old ones—despite severe class imbalance. Existing methods struggle to balance stability and plasticity, often collapsing under extreme sample scarcity. To address this, we propose ViRN, a novel CL framework that integrates variational inference (VI) with distributional trilateration for robust long-tailed learning. First, we model class-conditional distributions via a Variational Autoencoder to mitigate bias toward head classes. Second, we reconstruct tail-class distributions via Wasserstein distance-based neighborhood retrieval and geometric fusion, enabling sample-efficient alignment of tail-class representations. Evaluated on six long-tailed classification benchmarks—including speech (e.g., rare acoustic events, accents) and image tasks—ViRN achieves a 10.24% average accuracy gain over state-of-the-art methods.