Gabriel Nobis

Abstract

Diffusion models have excelled at capturing data distributions, but they still face limitations such as slow convergence, mode collapse on imbalanced data, and a lack of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments.
In this talk, we present our framework for replacing BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index $H \in (0,1)$, where $H=1/2$ recovers the classical BM. To ensure tractable inference and learning, we employ a recently popularized Markov approximation of fBM (MA-fBM) and derive its reverse time model, resulting in generative fractional diffusion models (GFDMs). We characterize the forward dynamics using a continuous reparameterization trick and propose an augmented score matching loss to efficiently learn the score-function, at minimal added cost. The ability to drive our diffusion model via MA-fBM provides flexibility and control. $H \leq 1/2$ enters the regime of rough paths whereas $H>1/2$ regularizes diffusion paths. The Markov approximation allows added control by varying the number of Markov processes linearly combined to approximate fBM. Our evaluations on real image datasets demonstrate that GFDM achieves greater pixel-wise diversity and enhanced image quality, as indicated by a lower FID, offering a promising alternative to traditional diffusion models.

Our speaker

Gabriel Nobis is a PhD student in the Department of Artificial Intelligence at Fraunhofer HHI. He studied mathematics and computer science at the Technical University of Berlin with focus on stochastic processes and machine learning. His primary research interests lie in the study of fractional noise for generative modelling and the application of diffusion models in the life sciences and the medical field.

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