Abstrakti
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. Code available here.
Alkuperäiskieli | Englanti |
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Otsikko | Advances in Neural Information Processing Systems 36 (NeurIPS 2023) |
Kustantaja | Curran Associates Inc. |
Sivumäärä | 31 |
ISBN (elektroninen) | 978-1-7138-9992-1 |
Tila | Julkaistu - 2024 |
OKM-julkaisutyyppi | A4 Artikkeli konferenssijulkaisussa |
Tapahtuma | Conference on Neural Information Processing Systems - Ernest N. Morial Convention Center, New Orleans, Yhdysvallat Kesto: 10 jouluk. 2023 → 16 jouluk. 2023 Konferenssinumero: 37 https://nips.cc/ |
Julkaisusarja
Nimi | Advances in Neural Information Processing Systems |
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Kustantaja | Morgan Kaufmann Publishers |
Vuosikerta | 36 |
ISSN (painettu) | 1049-5258 |
Conference
Conference | Conference on Neural Information Processing Systems |
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Lyhennettä | NeurIPS |
Maa/Alue | Yhdysvallat |
Kaupunki | New Orleans |
Ajanjakso | 10/12/2023 → 16/12/2023 |
www-osoite |