Image Interpolation with Score-based Riemannian Metrics of Diffusion Models

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.

@article{saito2025_2504.20288,
  title={ Image Interpolation with Score-based Riemannian Metrics of Diffusion Models },
  author={ Shinnosuke Saito and Takashi Matsubara },
  journal={arXiv preprint arXiv:2504.20288},
  year={ 2025 }
}