Recent studies have shown that Joint Denoising and Super-Resolution (JDSR) approaches can produce high-quality medical images. However, obtaining ground truth images for training is often infeasible in fluorescence microscopy (FM). Moreover, current JDSR methods can be impractical as they only rely on a fixed scale for resolution. Existing methods aim to learn a direct mapping between low-quality input and high-quality output in pixel space. In this paper, we introduce the Continuous Diffusion Model. This novel self-supervised method iteratively retrieves a noise-free image in continuous space, enabling us to generate clean images at any arbitrary resolutions. Our quantitative analysis confirms the effectiveness of our proposed method. We outperformed both supervised and self-supervised methods by an average of \(30.5\%/7.4\%\) in terms of RMSE/SSIM. Our output preserves fine details and structures better than other state-of-the-art methods, as demonstrated by the qualitative analysis. The source code is available at https://github.com/colinsctsang/ContinuousDiffusionModel .