mlsanityData to 7 Oct 2026

Unsupervised learning of anomalous diffusion data

arXiv 2108.03411 ↗First posted 7 Aug 2021cond-mat.stat-mech cs.LG physics.bio-phcited by 8

On the map: Diffusion models → Diffusion foundations and sampling

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.

Key facts. Cited by 8 papers in the map (data through 7 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.

Builds on

6 of 45 references.

References · 6

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019Deep Learning for Anomaly Detection: A Surveycited by 357
  4. 2019Generalization Bounds For Unsupervised and Semi-Supervised Learning With Autoencoderscited by 11
  5. 2021Learning physical properties of anomalous random walks using graph neural networkscited by 10
  6. 2021WaveNet-Based Deep Neural Networks for the Characterization of Anomalous Diffusion (WADNet)cited by 7

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Citing papers per year: 2023: 3; 2024: 3; 2025: 2.

8 papers.

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  1. 2021Extreme Learning Machine for the Characterization of Anomalous Diffusion from Single Trajectories (AnDi-ELM)
  2. 2025Quantifying the Ease of Reproducing Training Data in Unconditional Diffusion Models
  3. 2025Physics-Informed Diffusion Models for Unsupervised Anomaly Detection in Multivariate Time Series
  4. 2026Rethinking the Diffusion Model from a Langevin Perspective
  5. 2025Learning What Matters: Steering Diffusion via Spectrally Anisotropic Forward Noise
  6. 2024Exploring how deep learning decodes anomalous diffusion via Grad-CAM
  7. 2026Sticky Jump Diffusions: A Unifying View of Masked, Continuous, and Hybrid Diffusion
  8. 2024Demystifying Variational Diffusion Models