  Spectral Graph Neural Networks (GNNs) have achieved tremendous success in
graph machine learning, with polynomial filters applied for graph convolutions,
where all nodes share the identical filter weights to mine their local
contexts. Despite the success, existing spectral GNNs usually fail to deal with
complex networks (e.g., WWW) due to such homogeneous spectral filtering setting
that ignores the regional heterogeneity as typically seen in real-world
networks. To tackle this issue, we propose a novel diverse spectral filtering
(DSF) framework, which automatically learns node-specific filter weights to
exploit the varying local structure properly. Particularly, the diverse filter
weights consist of two components -- A global one shared among all nodes, and a
local one that varies along network edges to reflect node difference arising
from distinct graph parts -- to balance between local and global information.
As such, not only can the global graph characteristics be captured, but also
the diverse local patterns can be mined with awareness of different node
positions. Interestingly, we formulate a novel optimization problem to assist
in learning diverse filters, which also enables us to enhance any spectral GNNs
with our DSF framework. We showcase the proposed framework on three
state-of-the-arts including GPR-GNN, BernNet, and JacobiConv. Extensive
experiments over 10 benchmark datasets demonstrate that our framework can
consistently boost model performance by up to 4.92% in node classification
tasks, producing diverse filters with enhanced interpretability. Code is
available at \url{https://github.com/jingweio/DSF}.
