mlsanityData to 7 Oct 2026

Local Hessian Spectral Filtering for Robust Intrinsic Dimension Estimation

arXiv 2605.01221 ↗First posted 2 May 2026cs.LGcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

While diffusion models enable new approaches for estimating Local Intrinsic Dimension (LID), existing methods fail in high-dimensional spaces where noise from vast normal directions overwhelms the tangent signal. We propose Local Hessian Spectral Dimension (LHSD), which resolves this by applying spectral filtering to the log-density Hessian, explicitly cutting off large eigenvalues associated with normal directions to count zero-curvature tangent directions. Implemented using Stochastic Lanczos Quadrature (SLQ), LHSD avoids full Hessian construction, achieving linear scalability with dimension D. Experiments on synthetic and real data confirm LHSD's superior robustness and its utility in detecting memorization in large-scale diffusion models. The code is available at github.com/geosada/LHSD

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 20 of its 42 references that are in the map. First posted on arXiv 2 May 2026.

Builds on

20 of 42 references.

Closest ancestors · 5

Same direction, newest first

  1. 2025On Convolutions, Intrinsic Dimension, and Diffusion Models25 Jun
  2. 2024Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes5 Dec
  3. 2024Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusion8 Oct
  4. 2024A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models5 Jun
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec

Other references · 15

  1. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,131
  2. 2023Extracting Training Data from Diffusion Modelscited by 723
  3. 2019An Investigation into Neural Net Optimization via Hessian Eigenvalue Densitycited by 289
  4. 2014Identifying and attacking the saddle point problem in high-dimensional non-convex optimizationcited by 286
  5. 2018Characterizing Adversarial Subspaces Using Local Intrinsic Dimensionalitycited by 280
  6. 2019Intrinsic dimension of data representations in deep neural networkscited by 276
  7. 2018Estimating the intrinsic dimension of datasets by a minimal neighborhood informationcited by 246
  8. 2022A Self-Supervised Descriptor for Image Copy Detectioncited by 175
  9. 2016Eigenvalues of the Hessian in Deep Learning: Singularity and Beyondcited by 156
  10. 2021Scikit-dimension: a Python package for intrinsic dimension estimationcited by 68
  11. 2022Verifying the Union of Manifolds Hypothesis for Image Datacited by 62
  12. 2024A Geometric Framework for Understanding Memorization in Generative Modelscited by 40
3 more
  1. 2024A Geometric Explanation of the Likelihood OOD Detection Paradoxcited by 22
  2. 2021Analysis of stochastic Lanczos quadrature for spectrum approximationcited by 17
  3. 2024A Wiener Process Perspective on Local Intrinsic Dimension Estimation Methodscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Minimax Lower Bound for Estimating Diffusion-based Local Intrinsic Dimensioncited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Connection Between Score Matching and Local Intrinsic Dimension
  2. 2026Intrinsic-Hybrid Latent Diffusion Models for Generative Modeling on Unknown Manifolds
  3. 2025Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models
  4. 2024Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions
  5. 2026Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
  6. 2026PTL-Diffusion: Manifold-Aware Diffusion with Periodic Terminal Laws
  7. 2026First Learn, Then Memorize: The Spectral Bias of Diffusion Models
  8. 2026Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions