Linear Diffusion Networks: Harnessing Diffusion Processes for Global Interactions

Diffusion kernels capture global dependencies. We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a diffusion-inspired attention mechanism. This design enables efficient global information propagation while preserving fine-grained temporal details. LDN overcomes the limitations of conventional recurrent and transformer models by allowing full parallelization across time steps and supporting robust multi-scale temporal representations. Experiments on benchmark sequence modeling tasks demonstrate that LDN delivers superior performance and scalability, setting a new standard for global interaction in sequential data.