# A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methods

arXiv: https://arxiv.org/abs/2406.17125 · HTML: https://mlsanity.com/paper/2406.17125/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 13 of 13)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models](https://mlsanity.com/paper/2406.03537/) (2024)
- [LIDL: Local Intrinsic Dimension Estimation Using Approximate Likelihood](https://mlsanity.com/paper/2206.14882/) (2022)
- [On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models](https://mlsanity.com/paper/2402.03845/) (2024)
- [On the Latent Space of Wasserstein Auto-Encoders](https://mlsanity.com/paper/1802.03761/) (2018)
- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [Learning Manifold Dimensions with Conditional Variational Autoencoders](https://mlsanity.com/paper/2302.11756/) (2023)
- [Adversarial Estimation of Topological Dimension with Harmonic Score Maps](https://mlsanity.com/paper/2312.06869/) (2023)

## Built on by (most cited first, 1 of 1)

- [Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation](https://mlsanity.com/paper/2605.01221/) (2026)

## Abstract (arXiv)

Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use generative models to approximate diffused dataset density to scale the methods to high-dimensional datasets (e.g. images). In this paper, we investigate the recent state-of-the-art parametric LID estimation methods from the perspective of the Wiener process. We explore how these methods behave when their assumptions are not met. We give an extended mathematical description of those methods and their error as a function of the probability density of the data.