Functional Diffusion
This work addresses the challenge of handling irregular or non-standard data types like images, videos, and 3D shapes in a unified framework, representing an incremental advancement in diffusion models.
The authors tackled the problem of generative modeling for data represented by functions with continuous domains, proposing functional diffusion as a new class of diffusion models that extends classical methods to infinite-dimensional domains, and demonstrated generative results on signed distance functions and deformation functions on 3D surfaces.
We propose a new class of generative diffusion models, called functional diffusion. 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.