Image Interpolation with Score-based Riemannian Metrics of Diffusion Models

2025-04-28

AI Summary

Existing diffusion models fail to exploit the geometric structure of the implicitly learned data manifold, limiting the realism of image interpolation and editing as well as prompt fidelity. This paper introduces the first formulation of the data space of pre-trained diffusion models as a Riemannian manifold induced by the score function, enabling the construction of a differentiable, parameter-free intrinsic metric and a geodesic-based, geometry-aware interpolation method. The approach requires no fine-tuning or additional training and is inherently compatible with diverse diffusion architectures. Experiments on MNIST and Stable Diffusion demonstrate that our method yields interpolations with reduced noise, improved structural coherence, and significantly enhanced text-prompt fidelity—outperforming standard Euclidean interpolation and latent-space mapping strategies. Our core contribution is the establishment of the first Riemannian metric framework grounded in score matching, enabling explicit and computationally efficient exploitation of the geometric structure inherent in diffusion models.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning with Manifolds
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

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.

Problem

• Leveraging diffusion models' data manifold for interpolation
• Improving image interpolation realism and prompt faithfulness
• Developing Riemannian metric from score function for geometry-awareness

Innovation

• Treats diffusion model data space as Riemannian manifold
• Uses score function to derive manifold metric
• Produces realistic, prompt-faithful image interpolations