# Functional Diffusion Source: [Functional Diffusion]() Collection index: [llms.txt]() Data updated: 2026-01-04T04:37:00.117Z Authors: Biao Zhang, Peter Wonka Published: 2023-11-26T21:35:34.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [SDF prediction on 3D shapes sparse 64-point observations](): SDF prediction; 3D shapes sparse 64-point observations; Chamfer Distance: 0.101. - [Deformation field generation on Dynamic shape sequence (test)](): Deformation field generation; Dynamic shape sequence (test); MSE: 6.91. - [3D SDF Generation on ShapeNet (test)](): 3D SDF Generation; ShapeNet (test); Chamfer Distance: 0.101. ## Original sources and implementation [Original paper]() [PDF]()