Due to privacy and security concerns, recent advancements in group fairness advocate for model training regardless of demographic information. However, most methods still require prior knowledge of demographics. In this study, we explore the potential for achieving fairness without compromising its utility when no prior demographics are provided to the training set, namely \emph{harmless Rawlsian fairness}. We ascertain that such a fairness requirement with no prior demographic information essential promotes training losses to exhibit a Dirac delta distribution. To this end, we propose a simple but effective method named VFair to minimize the variance of training losses inside the optimal set of empirical losses. This problem is then optimized by a tailored dynamic update approach that operates in both loss and gradient dimensions, directing the model towards relatively fairer solutions while preserving its intact utility. Our experimental findings indicate that regression tasks, which are relatively unexplored from literature, can achieve significant fairness improvement through VFair regardless of any prior, whereas classification tasks usually do not because of their quantized utility measurements. The implementation of our method is publicly available at \url{https://github.com/wxqpxw/VFair}.