Recent advances in diffusion and flow-based generative models have demonstrated remarkable success in image restoration tasks, achieving superior perceptual quality compared to traditional deep learning approaches. However, these methods either require numerous sampling steps to generate high-quality images, resulting in significant computational overhead, or rely on common model distillation, which usually imposes a fixed fidelity-realism trade-off and thus lacks flexibility. In this paper, we introduce OFTSR, a novel flow-based framework for one-step image super-resolution that can produce outputs with tunable levels of fidelity and realism. Our approach first trains a conditional flow-based super-resolution model to serve as a teacher model. We then distill this teacher model by applying a specialized constraint. Specifically, we force the predictions from our one-step student model for same input to lie on the same sampling ODE trajectory of the teacher model. This alignment ensures that the student model's single-step predictions from initial states match the teacher's predictions from a closer intermediate state. Through extensive experiments on datasets including FFHQ (256$\times$256), DIV2K, and ImageNet (256$\times$256), we demonstrate that OFTSR achieves state-of-the-art performance for one-step image super-resolution, while having the ability to flexibly tune the fidelity-realism trade-off. Codes: \href{https://github.com/yuanzhi-zhu/OFTSR}{https://github.com/yuanzhi-zhu/OFTSR}.

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