Continuous-Time Functional Diffusion Processes

Giulio Franzese, Giulio Corallo, Simone Rossi, Markus Heinonen, Maurizio Filippone, Pietro Michiardi

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference article in proceedingsScientificvertaisarvioitu

1 Sitaatiot (Scopus)

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.

AlkuperäiskieliEnglanti
OtsikkoAdvances in Neural Information Processing Systems 36 (NeurIPS 2023)
KustantajaCurran Associates Inc.
Sivumäärä31
ISBN (elektroninen)978-1-7138-9992-1
TilaJulkaistu - 2024
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaConference on Neural Information Processing Systems - Ernest N. Morial Convention Center, New Orleans, Yhdysvallat
Kesto: 10 jouluk. 202316 jouluk. 2023
Konferenssinumero: 37
https://nips.cc/

Julkaisusarja

NimiAdvances in Neural Information Processing Systems
KustantajaMorgan Kaufmann Publishers
Vuosikerta36
ISSN (painettu)1049-5258

Conference

ConferenceConference on Neural Information Processing Systems
LyhennettäNeurIPS
Maa/AlueYhdysvallat
KaupunkiNew Orleans
Ajanjakso10/12/202316/12/2023
www-osoite

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