Abstract : The formulation of Diffusion Curves [Orzan et al. 2008] allows for the flexible creation of vector graphics images from a set of curves and colors: a diffusion process fills out the parts of the image that are away from curves. However, this model has limitations in certain situations and does not always seem to agree with how an artist wants to use the software. First, the diffusion itself cannot be controlled, only the colors. Further, the fact that color needs to be defined everywhere along the curve can lead to tedious and nonintuitive interactions. In this paper, we present a number of adaptations to diffusion curves that constrain how color is spread across the image. Specifically, we argue for the utility of controlling the speed and direction of the color diffusion, and the ability to have barriers that can be defined without the need to specify a particular color along these curves. We also describe how this can be implemented by solving a linear system, and demonstrate the effectiveness of our solution on a number of examples.