LocDiffusion: Identifying Locations on Earth by Diffusing in the Hilbert Space

2025-03-23

AI Summary

Image geolocation aims to infer the geographic coordinates where an image was captured; however, existing grid-based classification or retrieval methods suffer significant performance degradation under test-time distribution shifts. This paper introduces LocDiffusion, the first generative diffusion model for geolocation—specifically, a conditional latent diffusion model that departs from conventional discriminative paradigms. Key contributions include: (i) the novel Spherical Harmonic Dirac Delta (SHDD) representation for location encoding/decoding directly on the sphere, eliminating manifold re-projection; (ii) a SIREN-enhanced CS-UNet architecture with spherical harmonic positional embeddings; and (iii) a Hilbert-space pattern-search decoder coupled with a latent-space KL-divergence optimization objective. Evaluated on standard benchmarks, LocDiffusion achieves state-of-the-art performance and demonstrates markedly improved generalization to unseen geographic locations, validating the efficacy and robustness of the generative geolocation paradigm.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services

Abstract

Image geolocalization is a fundamental yet challenging task, aiming at inferring the geolocation on Earth where an image is taken. Existing methods approach it either via grid-based classification or via image retrieval. Their performance significantly suffers when the spatial distribution of test images does not align with such choices. To address these limitations, we propose to leverage diffusion as a mechanism for image geolocalization. To avoid the problematic manifold reprojection step in diffusion, we developed a novel spherical positional encoding-decoding framework, which encodes points on a spherical surface (e.g., geolocations on Earth) into a Hilbert space of Spherical Harmonics coefficients and decodes points (geolocations) by mode-seeking. We call this type of position encoding Spherical Harmonics Dirac Delta (SHDD) Representation. We also propose a novel SirenNet-based architecture called CS-UNet to learn the conditional backward process in the latent SHDD space by minimizing a latent KL-divergence loss. We train a conditional latent diffusion model called LocDiffusion that generates geolocations under the guidance of images -- to the best of our knowledge, the first generative model for image geolocalization by diffusing geolocation information in a hidden location embedding space. We evaluate our method against SOTA image geolocalization baselines. LocDiffusion achieves competitive geolocalization performance and demonstrates significantly stronger generalizability to unseen geolocations.

Problem

• Image geolocalization via diffusion in Hilbert space
• Overcoming spatial distribution misalignment in test images
• Generating geolocations using conditional latent diffusion model

Innovation

• Diffusion mechanism for image geolocalization
• Spherical Harmonics Dirac Delta (SHDD) Representation
• CS-UNet architecture for latent SHDD space