  Real-world data generation often involves complex inter-dependencies among
instances, violating the IID-data hypothesis of standard learning paradigms and
posing a challenge for uncovering the geometric structures for learning desired
instance representations. To this end, we introduce an energy constrained
diffusion model which encodes a batch of instances from a dataset into
evolutionary states that progressively incorporate other instances' information
by their interactions. The diffusion process is constrained by descent criteria
w.r.t.~a principled energy function that characterizes the global consistency
of instance representations over latent structures. We provide rigorous theory
that implies closed-form optimal estimates for the pairwise diffusion strength
among arbitrary instance pairs, which gives rise to a new class of neural
encoders, dubbed as DIFFormer (diffusion-based Transformers), with two
instantiations: a simple version with linear complexity for prohibitive
instance numbers, and an advanced version for learning complex structures.
Experiments highlight the wide applicability of our model as a general-purpose
encoder backbone with superior performance in various tasks, such as node
classification on large graphs, semi-supervised image/text classification, and
spatial-temporal dynamics prediction.
