  Implicit neural fields, typically encoded by a multilayer perceptron (MLP)
that maps from coordinates (e.g., xyz) to signals (e.g., signed distances),
have shown remarkable promise as a high-fidelity and compact representation.
However, the lack of a regular and explicit grid structure also makes it
challenging to apply generative modeling directly on implicit neural fields in
order to synthesize new data. To this end, we propose HyperDiffusion, a novel
approach for unconditional generative modeling of implicit neural fields.
HyperDiffusion operates directly on MLP weights and generates new neural
implicit fields encoded by synthesized MLP parameters. Specifically, a
collection of MLPs is first optimized to faithfully represent individual data
samples. Subsequently, a diffusion process is trained in this MLP weight space
to model the underlying distribution of neural implicit fields. HyperDiffusion
enables diffusion modeling over a implicit, compact, and yet high-fidelity
representation of complex signals across 3D shapes and 4D mesh animations
within one single unified framework.
