mlsanityData to 7 Oct 2026

Geometric Decoupling: Diagnosing the Structural Instability of Latent

arXiv 2604.18804 ↗First posted 20 Apr 2026cs.CV cs.AIcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the generative Jacobian, decomposing geometry into textitLocal Scaling (capacity) and textitLocal Complexity (curvature). Our study uncovers a ``Geometric Decoupling": while curvature in normal generation functionally encodes image detail, OOD generation exhibits a functional decoupling where extreme curvature is wasted on unstable semantic boundaries rather than perceptible details. This geometric misallocation identifies ``Geometric Hotspots" as the structural root of instability, providing a robust intrinsic metric for diagnosing generative reliability.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 39 of its 53 references that are in the map. First posted on arXiv 20 Apr 2026.

Builds on

39 of 53 references.

Closest ancestors · 11

Same direction, newest first

  1. 2025Diffusion Models and the Manifold Hypothesis: Log-Domain Smoothing is Geometry Adaptive2 Oct
  2. 2024What Secrets Do Your Manifolds Hold? Understanding the Local Geometry of Generative Models15 Aug
  3. 2024A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models5 Jun
  4. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesis5 Mar
  5. 2023Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models7 Dec
  6. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry24 Jul
  7. 2023SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis4 Jul
  8. 2022Diffusion Models already have a Semantic Latent Space20 Oct
  9. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Implicit Models6 Oct

Other references · 28

  1. 2014Microsoft COCO: Common Objects in Contextcited by 17,498
  2. 2022DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generationcited by 3,286
  3. 2022Prompt-to-Prompt Image Editing with Cross Attention Controlcited by 2,409
  4. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  5. 2022Null-text Inversion for Editing Real Images using Guided Diffusion Modelscited by 1,168
  6. 2022Plug-and-Play Diffusion Features for Text-Driven Image-to-Image Translationcited by 897
  7. 2017Spectrally-normalized margin bounds for neural networkscited by 681
  8. 2018Do Deep Generative Models Know What They Don't Know?cited by 443
  9. 2021Understanding Dimensional Collapse in Contrastive Self-supervised Learningcited by 374
  10. 2022Inversion-Based Style Transfer with Diffusion Modelscited by 290
  11. 2022EDICT: Exact Diffusion Inversion via Coupled Transformationscited by 256
  12. 2019Representation Degeneration Problem in Training Natural Language Generation Modelscited by 250
16 more
  1. 2017PixelDefend: Leveraging Generative Models to Understand and Defend against Adversarial Examplescited by 243
  2. 2020Why Normalizing Flows Fail to Detect Out-of-Distribution Datacited by 220
  3. 2019Complexity of Linear Regions in Deep Networkscited by 166
  4. 2018Efficient GAN-Based Anomaly Detectioncited by 122
  5. 2024Understanding Hallucinations in Diffusion Models through Mode Interpolationcited by 87
  6. 2021Rectangular Flows for Manifold Learningcited by 49
  7. 2025Hallucination Detection in LLMs Using Spectral Features of Attention Mapscited by 42
  8. 2022A Geometric Perspective on Variational Autoencoderscited by 24
  9. 2026Forest Before Trees: Latent Superposition for Efficient Visual Reasoningcited by 16
  10. 2023On Explicit Curvature Regularization in Deep Generative Modelscited by 13
  11. 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 12
  12. 2025Mitigating Hallucinations in Diffusion Models through Adaptive Attention Modulationcited by 11
  13. 2024On the Local Complexity of Linear Regions in Deep ReLU Networkscited by 9
  14. 2021Provable Lipschitz Certification for Generative Modelscited by 7
  15. 2021Manifold Matching via Deep Metric Learning for Generative Modelingcited by 3
  16. 2024Analyzing Generative Models by Manifold Entropic Metricscited by 2

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