In this paper we put forward a novel extension of the classic Max-Sum algorithm to the framework of Continuous Distributed Constrained Optimization Problems (Continuous DCOPs), by utilizing a popular geometric algorithm, namely Quadtrees. In its standard form, Max-Sum can only solve Continuous DCOPs with an a priori discretization procedure. Existing Max-Sum extensions to continuous multiagent coordination domains require additional assumptions regarding the form of the factors, such as access to the gradient, or the ability to model them as continuous piecewise linear functions. Our proposed approach has no such requirements: we model the exchanged messages with Quadtrees, and, as such, the discretization procedure is dynamic and embedded in the internal Max-Sum operations (addition and marginal maximization). We apply Max-Sum with Quadtrees to lane-free autonomous driving. Our experimental evaluation showcases the effectiveness of our approach in this challenging coordination domain.