Diffusion models have proven effective for various applications such as images, audio and graph generation. Other important applications are image super-resolution and the solution of inverse problems. More recently, some works have used stochastic differential equations (SDEs) to generalize diffusion models to continuous time. In this work, we introduce SDEs to generate super-resolution face images. To the best of our knowledge, this is the first time SDEs have been used for such an application. The proposed method provides an improved peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), and consistency than the existing super-resolution methods based on diffusion models. In particular, we also assess the potential application of this method for the face recognition task. A generic facial feature extractor is used to compare the super-resolution images with the ground truth and superior results were obtained compared with other methods. Our code is publicly available at https://github.com/marcelowds/sr-sde
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