Generative fractional diffusion models
File(s)
Author(s)
Type
Conference Paper
Abstract
We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion
models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack
of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments. In this paper, we replace BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index H ∈ (0, 1), where H = 0.5 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
(GFDM). We characterize the forward dynamics using a continuous reparameterization trick and propose augmented score matching to efficiently learn the score
function, which is partly known in closed form, at minimal added cost. The ability to drive our diffusion model via MA-fBM offers flexibility and control. H ≤ 0.5 enters the regime of rough paths whereas H > 0.5 regularizes diffusion paths
and invokes long-term memory. 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 models1.
models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack
of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments. In this paper, we replace BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index H ∈ (0, 1), where H = 0.5 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
(GFDM). We characterize the forward dynamics using a continuous reparameterization trick and propose augmented score matching to efficiently learn the score
function, which is partly known in closed form, at minimal added cost. The ability to drive our diffusion model via MA-fBM offers flexibility and control. H ≤ 0.5 enters the regime of rough paths whereas H > 0.5 regularizes diffusion paths
and invokes long-term memory. 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 models1.
Date Issued
2024-12-10
Date Acceptance
2024-09-18
Citation
Advances in Neural Information Processing Systems 37, 2024, pp.25469-25509
ISBN
9798331314385
Publisher
Curran Associates, Inc.
Start Page
25469
End Page
25509
Journal / Book Title
Advances in Neural Information Processing Systems 37
Copyright Statement
© 2024 The Author(s).
Source
38th Conference on Neural Information Processing Systems (NeurIPS 2024)
Publication Status
Published
Start Date
2024-12-10
Finish Date
2024-12-15
Coverage Spatial
Vancouver, Canada