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.
View on arXiv@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 }
}