Foundation models enable prompt-based classifiers for zero-shot and few-shot learning. Nonetheless, the conventional method of employing fixed prompts suffers from distributional shifts that negatively impact generalizability to unseen samples. This paper introduces prompt diffusion, which uses a diffusion model to gradually refine the prompts to obtain a customized prompt for each sample. Specifically, we first optimize a collection of prompts to obtain over-fitted prompts per sample. Then, we propose a prompt diffusion model within the prompt space, enabling the training of a generative transition process from a random prompt to its overfitted prompt. As we cannot access the label of a test image during inference, our model gradually generates customized prompts solely from random prompts using our trained, prompt diffusion. Our prompt diffusion is generic, flexible, and modality-agnostic, making it a simple plug-and-play module seamlessly embedded into existing prompt learning methods for textual, visual, or multi-modal prompt learning. Our diffusion model uses a fast ODE-based sampling strategy to optimize test sample prompts in just five steps, offering a good trade-off between performance improvement and computational efficiency. For all prompt learning methods tested, adding prompt diffusion yields more robust results for base-to-new generalization, cross-dataset generalization, and domain generalization in classification tasks tested over 15 diverse datasets.