Modern generative models still lack human-level creativity, particularly in multi-branch diversity. Prior approaches to address this problem often incur heavy computation or strong dependency on model architecture. Therefore, we introduce UAG(Universal Avoidance Generation), a model-agnostic and computationally efficient generation strategy that penalizes similarity among previously generated outputs. Thus, UAG can enhance multi-branch diversity across both diffusion and transformer models, with minimal additional computation. In experiments, our method achieves up to 1.9 times higher diversity, runs 4.4 times faster, and requires only 1/64 of the FLOPs compared to state-of-the-art methods. The full code is https://anonymous.4open.science/r/2026_ACL_Universal/.