While Graph Neural Networks (GNNs) are widely used in modern computational biology, an underexplored drawback of common GNN methods,is that they are not inherently multiscale consistent: Two graphs describing the same object or situation at different resolution scales are assigned vastly different latent representations. This prevents graph networks from generating data representations that are consistent across scales. It also complicates the integration of representations at the molecular scale with those generated at the biological scale.Here we discuss why existing GNNs struggle with multiscale consistency and show how to overcome this problem by modifying the message passing paradigm within GNNs.