Functional Diffusion

We propose functional diffusion a generative diffusion model focused on infinite-dimensional function data samples. In contrast to previous work functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be seen as an extension of classical diffusion models to an infinite-dimensional domain. Functional diffusion is very versatile as images videos audio 3D shapes deformations etc. can be handled by the same framework with minimal changes. In addition functional diffusion is especially suited for irregular data or data defined in non-standard domains. In our work we derive the necessary foundations for functional diffusion and propose a first implementation based on the transformer architecture. We show generative results on complicated signed distance functions and deformation functions defined on 3D surfaces.