Audio Super-Resolution is a set of techniques aimed at high-quality estimation of the given signal as if it would be sampled with higher sample rate. Among suggested methods there are diffusion and flow models (which are considered slower), generative adversarial networks (which are considered faster), however both approaches are currently presented by high-parametric networks, requiring high computational costs both for training and inference. We propose a solution to both these problems by re-considering the recent advances in the training of diffusion models and applying them to super-resolution from any to 48 kHz sample rate. Our approach shows better results than NU-Wave 2 and is comparable to state-of-the-art models. Our model called FastWave has around 50 GFLOPs of computational complexity and 1.3 M parameters and can be trained with less resources and significantly faster than the majority of recently proposed diffusion- and flow-based solutions. The code has been made publicly available.