Abstract: Domain shift degrades classification models on new data distributions. Conventional unsupervised domain adaptation (UDA) aims to learn features that bridge labeled source and unlabeled target domains. In contrast to feature learning, gradual domain adaptation (GDA) leverages extra continuous intermediate domains with pseudo-labels to boost the source classifier. However, real intermediate domains are sometimes unavailable or ineffective. In this paper, we propose $\textbf{G}$radual Domain Adaptation via $\textbf{G}$radient $\textbf{F}$low (GGF) to generate intermediate domains with preserving labels, thereby enabling us a fine-tuning method for GDA. We employ the Wasserstein gradient flow in Kullback–Leibler divergence to transport samples from the source to the target domain. To simulate the dynamics, we utilize the Langevin algorithm. Since the Langevin algorithm disregards label information and introduces diffusion noise, we introduce classifier-based and sample-based potentials to avoid label switching and dramatic deviations in the sampling process. For the proposed GGF model, we analyze its generalization bound. Experiments on several benchmark datasets demonstrate the superiority of the proposed GGF method compared to state-of-the-art baselines.