In this work, we introduce Modulated Flows (ModFlows), a novel approach for color style transfer between images based on rectified flows. The primary goal of the color transfer is to adjust the colors of a target image to match the color distribution of a reference image. Our technique is based on optimal transport and executes color transfer as an invertible transformation within the RGB color space. The ModFlows utilizes the bijective property of flows, enabling us to introduce a common intermediate color distribution and build a dataset of rectified flows. We train an encoder on this dataset to predict the weights of a rectified model for unseen images. We show that the trained encoder provides an image embedding, associated only with its color style. The presented method is capable of processing 4K images and achieves the state-of-the-art performance in terms of content and style similarity.