# LocDiff: Identifying Locations on Earth by Diffusing in the Hilbert Space arXiv: https://arxiv.org/abs/2503.18142 ยท HTML: https://mlsanity.com/paper/2503.18142/ ## Key facts - Cited by 6 papers in the map (data through 14 Oct 2026). - Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models. - Builds on 35 of its 50 references that are in the map. - First posted on arXiv 23 Mar 2025. ## Placed in - Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/) ## Builds on (most cited first, 30 of 35) - [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021) - [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020) - [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020) - [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020) - [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020) - [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022) - [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020) - [GeoCLIP: Clip-Inspired Alignment between Locations and Images for Effective Worldwide Geo-localization](https://mlsanity.com/paper/2309.16020/) (2023) - [Geometric Latent Diffusion Models for 3D Molecule Generation](https://mlsanity.com/paper/2305.01140/) (2023) - [SatCLIP: Global, General-Purpose Location Embeddings with Satellite Imagery](https://mlsanity.com/paper/2311.17179/) (2023) - [Where am I looking at? Joint Location and Orientation Estimation by Cross-View Matching](https://mlsanity.com/paper/2005.03860/) (2020) - [Riemannian Diffusion Models](https://mlsanity.com/paper/2208.07949/) (2022) - [PlaNet - Photo Geolocation with Convolutional Neural Networks](https://mlsanity.com/paper/1602.05314/) (2016) - [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019) - [R2Former: Unified Retrieval and Reranking Transformer for Place Recognition](https://mlsanity.com/paper/2304.03410/) (2023) - [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020) - [Revisiting IM2GPS in the Deep Learning Era](https://mlsanity.com/paper/1705.04838/) (2017) - [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023) - [CPlaNet: Enhancing Image Geolocalization by Combinatorial Partitioning of Maps](https://mlsanity.com/paper/1808.02130/) (2018) - [Moser Flow: Divergence-based Generative Modeling on Manifolds](https://mlsanity.com/paper/2108.08052/) (2021) - [Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks](https://mlsanity.com/paper/2310.06743/) (2023) - [Spatial Implicit Neural Representations for Global-Scale Species Mapping](https://mlsanity.com/paper/2306.02564/) (2023) - [Where in the World is this Image? Transformer-based Geo-localization in the Wild](https://mlsanity.com/paper/2204.13861/) (2022) - [PIGEON: Predicting Image Geolocations](https://mlsanity.com/paper/2307.05845/) (2023) - [Where We Are and What We're Looking At: Query Based Worldwide Image Geo-localization Using Hierarchies and Scenes](https://mlsanity.com/paper/2303.04249/) (2023) - [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021) - [Sphere2Vec: A General-Purpose Location Representation Learning over a Spherical Surface for Large-Scale Geospatial Predictions](https://mlsanity.com/paper/2306.17624/) (2023) - [OpenStreetView-5M: The Many Roads to Global Visual Geolocation](https://mlsanity.com/paper/2404.18873/) (2024) - [Improving Image Classification with Location Context](https://mlsanity.com/paper/1505.03873/) (2015) - [Img2Loc: Revisiting Image Geolocalization using Multi-modality Foundation Models and Image-based Retrieval-Augmented Generation](https://mlsanity.com/paper/2403.19584/) (2024) ## Built on by (most cited first, 6 of 6) - [Localized, High-resolution Geographic Representations with Slepian Functions](https://mlsanity.com/paper/2602.00392/) (2026) - [HierLoc: Hyperbolic Entity Embeddings for Hierarchical Visual Geolocation](https://mlsanity.com/paper/2601.23064/) (2026) - [Skill-Conditioned Visual Geolocation for Vision-Language Models](https://mlsanity.com/paper/2604.09025/) (2026) - [GeoRouter: Dynamic Paradigm Routing for Worldwide Image Geolocalization](https://mlsanity.com/paper/2603.24376/) (2026) - [Pinpoint: Grounded Worldwide Image Geolocation via Cross-Source Retrieval and Reranking](https://mlsanity.com/paper/2606.04133/) (2026) - [GeoBridge: Decoupled Semantic Conditioning for Generative Image Geolocalization](https://mlsanity.com/paper/2608.11838/) (2026) ## Abstract (arXiv) Image geolocalization is a fundamental yet challenging task, aiming at inferring the geolocation on Earth where an image is taken. State-of-the-art methods employ either grid-based classification or gallery-based image-location retrieval, whose spatial generalizability significantly suffers if the spatial distribution of test images does not align with the choices of grids and galleries. Recently emerging generative approaches, while getting rid of grids and galleries, use raw geographical coordinates and suffer quality losses due to their lack of multi-scale information. To address these limitations, we propose a multi-scale latent diffusion model called LocDiff for image geolocalization. We developed a novel positional encoding-decoding framework called Spherical Harmonics Dirac Delta (SHDD) Representations, 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 on spherical probability distributions. We also propose a novel SirenNet-based architecture (CS-UNet) to learn an image-based conditional backward process in the latent SHDD space by minimizing a latent KL-divergence loss. To the best of our knowledge, LocDiff is the first image geolocalization model that performs latent diffusion in a multi-scale location encoding space and generates geolocations under the guidance of images. Experimental results show that LocDiff can outperform all state-of-the-art grid-based, retrieval-based, and diffusion-based baselines across 5 challenging global-scale image geolocalization datasets, and demonstrates significantly stronger generalizability to unseen geolocations.