  Procedural material graphs are a compact, parameteric, and
resolution-independent representation that are a popular choice for material
authoring. However, designing procedural materials requires significant
expertise and publicly accessible libraries contain only a few thousand such
graphs. We present MatFormer, a generative model that can produce a diverse set
of high-quality procedural materials with complex spatial patterns and
appearance. While procedural materials can be modeled as directed (operation)
graphs, they contain arbitrary numbers of heterogeneous nodes with
unstructured, often long-range node connections, and functional constraints on
node parameters and connections. MatFormer addresses these challenges with a
multi-stage transformer-based model that sequentially generates nodes, node
parameters, and edges, while ensuring the semantic validity of the graph. In
addition to generation, MatFormer can be used for the auto-completion and
exploration of partial material graphs. We qualitatively and quantitatively
demonstrate that our method outperforms alternative approaches, in both
generated graph and material quality.
