  In theory, diffusion curves promise complex color gradations for
infinite-resolution vector graphics. In practice, existing realizations suffer
from poor scaling, discretization artifacts, or insufficient support for rich
boundary conditions. Previous applications of the boundary element method to
diffusion curves have relied on polygonal approximations, which either forfeit
the high-order smoothness of B\'ezier curves, or, when the polygonal
approximation is extremely detailed, result in large and costly systems of
equations that must be solved. In this paper, we utilize the boundary integral
equation method to accurately and efficiently solve the underlying partial
differential equation. Given a desired resolution and viewport, we then
interpolate this solution and use the boundary element method to render it. We
couple this hybrid approach with the fast multipole method on a non-uniform
quadtree for efficient computation. Furthermore, we introduce an adaptive
strategy to enable truly scalable infinite-resolution diffusion curves.
