Synthetic time series generation is an emerging field of study in the broad spectrum of data science, addressing critical needs in diverse fields such as finance, meteorology, and healthcare. In recent years, diffusion methods have shown impressive results for image synthesis thanks to models such as Stable Diffusion and DALL·E, defining the new state-of-the-art methods. In time series generation, their potential exists but remains largely unexplored. In this work, we demonstrate the applicability and suitability of diffusion methods for time series generation on several datasets with a rigorous evaluation procedure. Our proposal, inspired from an existing diffusion model, obtained a better performance than a reference model based on generative adversarial networks (GANs). We also propose a modification of the model to allow for guiding the generation with respect to conditioning variables. This conditioned generation is successfully demonstrated on meteorological data.