mlsanityData to 14 Oct 2026

Image Interpolation with Score-based Riemannian Metrics of Diffusion Models

arXiv 2504.20288 ↗First posted 28 Apr 2025cs.CVcited by 4

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models excel in content generation by implicitly learning the data manifold, yet they lack a practical method to leverage this manifold - unlike other deep generative models equipped with latent spaces. This paper introduces a novel framework that treats the data space of pre-trained diffusion models as a Riemannian manifold, with a metric derived from the score function. Experiments with MNIST and Stable Diffusion show that this geometry-aware approach yields image interpolations that are more realistic, less noisy, and more faithful to prompts than existing methods, demonstrating its potential for improved content generation and editing.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 53 of its 64 references that are in the map. First posted on arXiv 28 Apr 2025.

Builds on

53 of 64 references.

Closest ancestors · 18

Same direction, newest first

  1. 2024Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusion8 Oct
  2. 2024A Geometric View of Data Complexity: Efficient Local Intrinsic Dimension Estimation with Diffusion Models5 Jun
  3. 2024Going beyond Compositions, DDPMs Can Produce Zero-Shot Interpolations29 May
  4. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections3 Apr
  5. 2024NoiseDiffusion: Correcting Noise for Image Interpolation with Diffusion Models beyond Spherical Linear Interpolation13 Mar
  6. 2024On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models6 Feb
  7. 2023Manifold Preserving Guided Diffusion28 Nov
  8. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry24 Jul
  9. 2023Hierarchical Diffusion Autoencoders and Disentangled Image Manipulation24 Apr
  10. 2023Unsupervised Discovery of Semantic Latent Directions in Diffusion Models24 Feb
  11. 2022Diffusion Models already have a Semantic Latent Space20 Oct
  12. 2022Understanding Diffusion Models: A Unified Perspective25 Aug
6 more
  1. 2022Score-Based Generative Models Detect Manifolds2 Jun
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  3. 2021Diffusion Autoencoders: Toward a Meaningful and Decodable Representation30 Nov
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Implicit Models6 Oct
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 35

  1. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,744
  2. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,177
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  4. 2016SGDR: Stochastic Gradient Descent with Warm Restartscited by 5,045
  5. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,025
  6. 2022Null-text Inversion for Editing Real Images using Guided Diffusion Modelscited by 1,179
  7. 2022Human Motion Diffusion Modelcited by 1,080
  8. 2022Exploring CLIP for Assessing the Look and Feel of Imagescited by 991
  9. 2024WorldSimBench: Towards Video Generation Models as World Simulatorscited by 881
  10. 2021DiffusionCLIP: Text-Guided Diffusion Models for Robust Image Manipulationcited by 642
  11. 2020GANSpace: Discovering Interpretable GAN Controlscited by 614
  12. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 508
23 more
  1. 2020Closed-Form Factorization of Latent Semantics in GANscited by 408
  2. 2023DreamSim: Learning New Dimensions of Human Visual Similarity using Synthetic Datacited by 337
  3. 2020Unsupervised Discovery of Interpretable Directions in the GAN Latent Spacecited by 289
  4. 2018Representer Point Selection for Explaining Deep Neural Networkscited by 187
  5. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 174
  6. 2017The Riemannian Geometry of Deep Generative Modelscited by 82
  7. 2021Input Similarity from the Neural Network Perspectivecited by 79
  8. 2023DiffMorpher: Unleashing the Capability of Diffusion Models for Image Morphingcited by 67
  9. 2017Metrics for Deep Generative Modelscited by 53
  10. 2021Low-Rank Subspaces in GANscited by 53
  11. 2020Geometrically Enriched Latent Spacescited by 45
  12. 2023Norm-guided latent space exploration for text-to-image generationcited by 43
  13. 2023Interpolating between Images with Diffusion Modelscited by 38
  14. 2021An error analysis of generative adversarial networks for learning distributionscited by 36
  15. 2022Region-Based Semantic Factorization in GANscited by 22
  16. 2023IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Modelscited by 21
  17. 2024Emergent Visual-Semantic Hierarchies in Image-Text Representationscited by 19
  18. 2024Diffusion State-Guided Projected Gradient for Inverse Problemscited by 14
  19. 2023On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldscited by 13
  20. 2021A prior-based approximate latent Riemannian metriccited by 11
  21. 2021Density estimation on low-dimensional manifolds: an inflation-deflation approachcited by 11
  22. 2024Diffusion Bridge AutoEncoders for Unsupervised Representation Learningcited by 6
  23. 2021Bayesian Quadrature on Riemannian Data Manifoldscited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025Learning a distance measure from the information-estimation geometry of datacited by 3
  2. 2025Which Way from B to A: The role of embedding geometry in image interpolation for Stable Diffusioncited by 1
  3. 2025FRAIN to Train: A Fast-and-Reliable Solution for Decentralized Federated Learningcited by 0
  4. 2026RemEdit: Efficient Diffusion Editing with Riemannian Geometrycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025What's Inside Your Diffusion Model? A Score-Based Riemannian Metric to Explore the Data Manifold
  2. 2025Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models
  3. 2026Diffusion Image Generation with Explicit Modeling of Data Manifold Geometry
  4. 2026Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity
  5. 2025MAD: Manifold Attracted Diffusion
  6. 2024Varying Manifolds in Diffusion: From Time-varying Geometries to Visual Saliency
  7. 2025Improving the Euclidean Diffusion Generation of Manifold Data by Mitigating Score Function Singularity
  8. 2023Diffusion Models for Constrained Domains