Papers › Continuous-Time Functional Diffusion Processes
Continuous-Time Functional Diffusion Processes
Giulio Franzese, Giulio Corallo, Simone Rossi, Markus Heinonen, Maurizio Filippone, Pietro Michiardi
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Image Generation | CelebA 64x64 | FDP(UViT) | FID | 11 | #26 of 39 | Archive leaderboard | report |
| Image Generation | CelebA 64x64 | FDP(UViT) | FID_CLIP | 6.55 | #26 of 39 | Archive leaderboard | report |
| Image Generation | CelebA 64x64 | FDP(MLP) | FID | 35 | #33 of 39 | Archive leaderboard | report |
| Image Generation | CelebA 64x64 | FDP(MLP) | FID_CLIP | 12.44 | #33 of 39 | Archive leaderboard | report |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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