Continual learning enables vision systems to adapt to ever-changing data distributions. Despite significant advances, existing approaches fail to capture continuous and concurrent shifts in classes and domains, a critical capability for real-world deployment. This work introduces Online VIL (Online Versatile Incremental Learning), a novel scenario where class concepts and visual domains evolve simultaneously online without explicit boundaries. To better adapt to the challenges of such dynamic environments that more closely resemble real-world conditions, we propose a novel framework TopFlow, Topology preservation with Flow matching representation that contains two complementary mechanisms: Domain-agnostic Flow Matching (DFM) and Global Topology Preservation (GTP). DFM guides the model to have domain-agnostic representations by integrating the geodesic flow kernel into contrastive learning. In contrast, GTP maintains the global structure of the feature space without explicitly storing past examples. Our extensive experiments demonstrate that TopFlow effectively addresses the limitations of existing methods within the Online VIL scenario, achieving state-of-the-art performance in challenging Online VIL. The proposed methods suggest potential directions for building continual learning systems in realistic dynamic environments. Our implementation code is available at https://github.com/KU-VGI/Online-VIL.

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