Speech emotion recognition (SER) is crucial in speech understanding and generation. Most approaches are based on either classification models or large language models. Different from previous methods, we propose Gen-SER, a novel approach that reformulates SER as a distribution shift problem via generative models. We propose to project discrete class labels into a continuous space, and obtain the terminal distribution via sinusoidal taxonomy encoding. The target-matching-based generative model is adopted to transform the initial distribution into the terminal distribution efficiently. The classification is achieved by calculating the similarity of the generated terminal distribution and ground truth terminal distribution. The experimental results confirm the efficacy of the proposed method, demonstrating its extensibility to various speech-understanding tasks and suggesting its potential applicability to a broader range of classification tasks.