Diffusion models have achieved impressive generative performance across diverse domains such as image, video, and scientific data generation. However, fine-tuning these models for new tasks remains challenging due to their large scale, architectural diversity, and high sensitivity to hyperparameters—particularly learning rates. In this work, we propose Wasserstein-Aware Transfer (WAT), a principled and effective fine-tuning strategy grounded in diffusion trajectory analysis and optimal transport theory. Our key insight is that the distributional discrepancies between diffusion trajectories from different datasets decrease progressively over time and converge near the noise end. Based on this observation, we introduce a class-wise matching mechanism that minimizes the Wasserstein distance between class distributions of source and target datasets. This enables alignment at the class level without modifying the standard fine-tuning pipeline. To further enhance knowledge retention, we propose a novel sampling strategy that linearly combines class-conditional outputs from both pretrained and fine-tuned models. This method is simple yet effective, requiring negligible computational overhead while preserving domain-specific and generalizable knowledge. Extensive experiments across seven diverse benchmarks demonstrate that WAT reliably enhances generation quality under distribution shifts, outperforming competitive baselines. These results underscore its robustness and affirm the potential of optimal transport as a principled basis for knowledge transfer in diffusion models.