Kuramoto Orientation Diffusion Models

Fuente: arXiv
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Main Authors: Song, Yue, Keller, T. Anderson, Brodjian, Sevan, Miyato, Takeru, Yue, Yisong, Perona, Pietro, Welling, Max
Format: Preprint
Published: 2025
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author Song, Yue
Keller, T. Anderson
Brodjian, Sevan
Miyato, Takeru
Yue, Yisong
Perona, Pietro
Welling, Max
author_facet Song, Yue
Keller, T. Anderson
Brodjian, Sevan
Miyato, Takeru
Yue, Yisong
Perona, Pietro
Welling, Max
contents Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role of phase synchronization in biological systems, we propose a score-based generative model built on periodic domains by leveraging stochastic Kuramoto dynamics in the diffusion process. In neural and physical systems, Kuramoto models capture synchronization phenomena across coupled oscillators -- a behavior that we re-purpose here as an inductive bias for structured image generation. In our framework, the forward process performs \textit{synchronization} among phase variables through globally or locally coupled oscillator interactions and attraction to a global reference phase, gradually collapsing the data into a low-entropy von Mises distribution. The reverse process then performs \textit{desynchronization}, generating diverse patterns by reversing the dynamics with a learned score function. This approach enables structured destruction during forward diffusion and a hierarchical generation process that progressively refines global coherence into fine-scale details. We implement wrapped Gaussian transition kernels and periodicity-aware networks to account for the circular geometry. Our method achieves competitive results on general image benchmarks and significantly improves generation quality on orientation-dense datasets like fingerprints and textures. Ultimately, this work demonstrates the promise of biologically inspired synchronization dynamics as structured priors in generative modeling.
format Preprint
id arxiv_https___arxiv_org_abs_2509_15328
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Kuramoto Orientation Diffusion Models
Song, Yue
Keller, T. Anderson
Brodjian, Sevan
Miyato, Takeru
Yue, Yisong
Perona, Pietro
Welling, Max
Machine Learning
Computer Vision and Pattern Recognition
Neurons and Cognition
Orientation-rich images, such as fingerprints and textures, often exhibit coherent angular directional patterns that are challenging to model using standard generative approaches based on isotropic Euclidean diffusion. Motivated by the role of phase synchronization in biological systems, we propose a score-based generative model built on periodic domains by leveraging stochastic Kuramoto dynamics in the diffusion process. In neural and physical systems, Kuramoto models capture synchronization phenomena across coupled oscillators -- a behavior that we re-purpose here as an inductive bias for structured image generation. In our framework, the forward process performs \textit{synchronization} among phase variables through globally or locally coupled oscillator interactions and attraction to a global reference phase, gradually collapsing the data into a low-entropy von Mises distribution. The reverse process then performs \textit{desynchronization}, generating diverse patterns by reversing the dynamics with a learned score function. This approach enables structured destruction during forward diffusion and a hierarchical generation process that progressively refines global coherence into fine-scale details. We implement wrapped Gaussian transition kernels and periodicity-aware networks to account for the circular geometry. Our method achieves competitive results on general image benchmarks and significantly improves generation quality on orientation-dense datasets like fingerprints and textures. Ultimately, this work demonstrates the promise of biologically inspired synchronization dynamics as structured priors in generative modeling.
title Kuramoto Orientation Diffusion Models
topic Machine Learning
Computer Vision and Pattern Recognition
Neurons and Cognition
url https://arxiv.org/abs/2509.15328