mlsanityData to 13 Oct 2026

Which Way from B to A: The role of embedding geometry in image interpolation for Stable Diffusion

arXiv 2511.12757 ↗First posted 16 Nov 2025cs.CV cs.AIcited by 1

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

It can be shown that Stable Diffusion has a permutation-invariance property with respect to the rows of Contrastive Language-Image Pretraining (CLIP) embedding matrices. This inspired the novel observation that these embeddings can naturally be interpreted as point clouds in a Wasserstein space rather than as matrices in a Euclidean space. This perspective opens up new possibilities for understanding the geometry of embedding space. For example, when interpolating between embeddings of two distinct prompts, we propose reframing the interpolation problem as an optimal transport problem. By solving this optimal transport problem, we compute a shortest path (or geodesic) between embeddings that captures a more natural and geometrically smooth transition through the embedding space. This results in smoother and more coherent intermediate (interpolated) images when rendered by the Stable Diffusion generative model. We conduct experiments to investigate this effect, comparing the quality of interpolated images produced using optimal transport to those generated by other standard interpolation methods. The novel optimal transport--based approach presented indeed gives smoother image interpolations, suggesting that viewing the embeddings as point clouds (rather than as matrices) better reflects and leverages the geometry of the embedding space.

Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 32 of its 50 references that are in the map. First posted on arXiv 16 Nov 2025.

Builds on

32 of 50 references.

Closest ancestors · 9

Same direction, newest first

  1. 2025Image Interpolation with Score-based Riemannian Metrics of Diffusion Models28 Apr
  2. 2025Probability Density Geodesics in Image Diffusion Latent Space9 Apr
  3. 2024Scaling Rectified Flow Transformers for High-Resolution Image Synthesis5 Mar
  4. 2023Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry24 Jul
  5. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  6. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  7. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  8. 2020Denoising Diffusion Implicit Models6 Oct
  9. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 23

  1. 2017Attention Is All You Needcited by 60,106
  2. 2021Learning Transferable Visual Models From Natural Language Supervisioncited by 33,588
  3. 2014Microsoft COCO: Common Objects in Contextcited by 17,550
  4. 2018The Unreasonable Effectiveness of Deep Features as a Perceptual Metriccited by 11,082
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 6,000
  6. 2022An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversioncited by 2,240
  7. 2018Computational Optimal Transportcited by 772
  8. 2023Ablating Concepts in Text-to-Image Diffusion Modelscited by 316
  9. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 311
  10. 2020Unsupervised Discovery of Interpretable Directions in the GAN Latent Spacecited by 288
  11. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 170
  12. 2022Diffusion Models Beat GANs on Topology Optimizationcited by 79
11 more
  1. 2023DiffMorpher: Unleashing the Capability of Diffusion Models for Image Morphingcited by 66
  2. 2024Get What You Want, Not What You Don't: Image Content Suppression for Text-to-Image Diffusion Modelscited by 63
  3. 2018Mad Max: Affine Spline Insights into Deep Learningcited by 54
  4. 2020Crisscrossed Captions: Extended Intramodal and Intermodal Semantic Similarity Judgments for MS-COCOcited by 46
  5. 2023Interpolating between Images with Diffusion Modelscited by 37
  6. 2024On Discrete Prompt Optimization for Diffusion Modelscited by 28
  7. 2024AID: Attention Interpolation of Text-to-Image Diffusioncited by 24
  8. 2023IMPUS: Image Morphing with Perceptually-Uniform Sampling Using Diffusion Modelscited by 20
  9. 2023Compositional Inversion for Stable Diffusion Modelscited by 19
  10. 2024TVG: A Training-free Transition Video Generation Method with Diffusion Modelscited by 15
  11. 2025Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMscited by 12

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Consistency Regularised Gradient Flows for Inverse Problemscited by 1

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  1. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers
  2. 2023GECCO: Geometrically-Conditioned Point Diffusion Models
  3. 2023Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models
  4. 2022Image Embedding for Denoising Generative Models
  5. 2022Unifying Diffusion Models' Latent Space, with Applications to CycleDiffusion and Guidance
  6. 2024DreamMover: Leveraging the Prior of Diffusion Models for Image Interpolation with Large Motion
  7. 2024Isometric Representation Learning for Disentangled Latent Space of Diffusion Models
  8. 2026Memorization In Stable Diffusion Is Unexpectedly Driven by CLIP Embeddings