mlsanityData to 14 Oct 2026

On Linear Interpolation in the Latent Space of Deep Generative Models

arXiv 2105.03663 ↗First posted 8 May 2021cs.LGcited by 8

Not on the map. Why?

Abstract (arXiv)

The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in latent space are associated with the quality of the underlying generative model. In this paper, we show that not all such interpolations are comparable as they can deviate arbitrarily from the shortest interpolation curve given by the geodesic. This deviation is revealed by computing curve lengths with the pull-back metric of the generative model, finding shorter curves than the straight line between endpoints, and measuring a non-zero relative length improvement on this straight line. This leads to a strategy to compare linear interpolations across two generative models. We also show the effect and importance of choosing an appropriate output space for computing shorter curves. For this computation we derive an extension of the pull-back metric.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 9 of its 14 references that are in the map. First posted on arXiv 8 May 2021.

Builds on

9 of 14 references.

References · 9

  1. 2013Auto-Encoding Variational Bayescited by 4,053
  2. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,588
  3. 2019Interpreting the Latent Space of GANs for Semantic Face Editingcited by 695
  4. 2020Unsupervised Discovery of Interpretable Directions in the GAN Latent Spacecited by 289
  5. 2017Latent Space Oddity: on the Curvature of Deep Generative Modelscited by 174
  6. 2019Inverting Deep Generative models, One layer at a timecited by 33
  7. 2019Fast and Robust Shortest Paths on Manifolds Learned from Datacited by 25
  8. 2018Geodesic Clustering in Deep Generative Modelscited by 14
  9. 2020Geodesics in fibered latent spaces: A geometric approach to learning correspondences between conditionscited by 2

Built on by

Cited by year

Citing papers per year: 2021: 1; 2022: 1; 2023: 0; 2024: 5; 2025: 1.

8 papers.

  1. 2025Action-Minimization Meets Generative Modeling: Efficient Transition Path Sampling with the Onsager-Machlup Functionalcited by 20
  2. 2024Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifoldscited by 13
  3. 2021Exploring the Latent Space of Autoencoders with Interventional Assayscited by 10
  4. 2024Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motionscited by 3
  5. 2022Optimized latent-code selection for explainable conditional text-to-image GANscited by 1
  6. 2024Generation of Geodesics with Actor-Critic Reinforcement Learning to Predict Midpointscited by 1
  7. 2024(Deep) Generative Geodesicscited by 1
  8. 2024Understanding Variational Autoencoders with Intrinsic Dimension and Information Imbalancecited by 1