# Unsupervised learning of anomalous diffusion data

arXiv: https://arxiv.org/abs/2108.03411 · HTML: https://mlsanity.com/paper/2108.03411/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 7 Aug 2021.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Generalization Bounds For Unsupervised and Semi-Supervised Learning With Autoencoders](https://mlsanity.com/paper/1902.01449/) (2019)
- [Learning physical properties of anomalous random walks using graph neural networks](https://mlsanity.com/paper/2103.11738/) (2021)
- [WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)](https://mlsanity.com/paper/2106.08887/) (2021)

## Built on by (most cited first, 8 of 8)

- [Learning minimal representations of stochastic processes with variational autoencoders](https://mlsanity.com/paper/2307.11608/) (2023)
- [Preface: Characterisation of Physical Processes from Anomalous Diffusion Data](https://mlsanity.com/paper/2301.00800/) (2023)
- [Machine Learning Analysis of Anomalous Diffusion](https://mlsanity.com/paper/2412.01393/) (2024)
- [Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories](https://mlsanity.com/paper/2308.09414/) (2023)
- [Multifractal-spectral features enhance classification of anomalous diffusion](https://mlsanity.com/paper/2401.07646/) (2024)
- [SPACE: SPAtial-aware Consistency rEgularization for anomaly detection in Industrial applications](https://mlsanity.com/paper/2411.05822/) (2024)
- [Bottom-up Iterative Anomalous Diffusion Detector (BI-ADD)](https://mlsanity.com/paper/2503.11529/) (2025)
- [Novelty detection on path space](https://mlsanity.com/paper/2512.03243/) (2025)

## Abstract (arXiv)

The characterization of diffusion processes is a keystone in our understanding of a variety of physical phenomena. Many of these deviate from Brownian motion, giving rise to anomalous diffusion. Various theoretical models exists nowadays to describe such processes, but their application to experimental setups is often challenging, due to the stochastic nature of the phenomena and the difficulty to harness reliable data. The latter often consists on short and noisy trajectories, which are hard to characterize with usual statistical approaches. In recent years, we have witnessed an impressive effort to bridge theory and experiments by means of supervised machine learning techniques, with astonishing results. In this work, we explore the use of unsupervised methods in anomalous diffusion data. We show that the main diffusion characteristics can be learnt without the need of any labelling of the data. We use such method to discriminate between anomalous diffusion models and extract their physical parameters. Moreover, we explore the feasibility of finding novel types of diffusion, in this case represented by compositions of existing diffusion models. At last, we showcase the use of the method in experimental data and demonstrate its advantages for cases where supervised learning is not applicable.