Deep Neural Networks (DNNs) tend to accrue technical debt and suffer from significant retraining costs when adapting to evolving requirements. Modularizing DNNs offers the promise of improving their reusability. Previous work has proposed techniques to decompose DNN models into modules both during and after training. However, these strategies yield several shortcomings, including significant weight overlaps and accuracy losses across modules, restricted focus on convolutional layers only, and added complexity and training time by introducing auxiliary masks to control modularity. In this work, we propose MODA, an activation-driven modular training approach. MODA promotes inherent modularity within a DNN model by directly regulating the activation outputs of its layers based on three modular objectives: intra-class affinity, inter-class dispersion, and compactness. MODA is evaluated using three well-known DNN models and five datasets with varying sizes. This evaluation indicates that, compared to the existing state-of-the-art, using MODA yields several advantages: (1) MODA accomplishes modularization with 22% less training time; (2) the resultant modules generated by MODA comprise up to 24x fewer weights and 37x less weight overlap while (3) preserving the original model's accuracy without additional fine-tuning; in module replacement scenarios, (4) MODA improves the accuracy of a target class by 12% on average while ensuring minimal impact on the accuracy of other classes.