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Weed management plays an important role in many modern agricultural applications. Conventional weed control methods mainly rely on chemical herbicides or hand weeding, which are often cost-ineffective, environmentally unfriendly, or even posing a threat to food safety and human health. Recently, automated/robotic weeding using machine vision systems has seen increased research attention with its potential for precise and individualized weed treatment. However, dedicated, large-scale, and labeled weed image datasets are required to develop robust and effective weed identification systems but they are often difficult and expensive to obtain. To address this issue, data augmentation approaches, such as generative adversarial networks (GANs), have been explored to generate highly realistic images for agricultural applications. Yet, despite some progress, those approaches are often complicated to train or have difficulties preserving fine details in images. In this paper, we present the first work of applying diffusion probabilistic models (also known as diffusion models) to generate high-quality synthetic weed images based on transfer learning. Comprehensive experimental results show that the developed approach consistently outperforms several state-of-the-art GAN models, representing the best trade-off between sample fidelity and diversity and highest FID score on a common weed dataset, CottonWeedID15. In addition, the expanding dataset with synthetic weed images can apparently boost model performance on four deep learning (DL) models for the weed classification tasks. Furthermore, the DL models trained on CottonWeedID15 dataset with only 10% of real images and 90% of synthetic weed images achieve a testing accuracy of over 94%, showing high-quality of the generated weed samples. The codes of this study are made publicly available at https://github.com/DongChen06/DMWeeds.