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LocDiff: Identifying Locations on Earth by Diffusing in the Hilbert Space
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Proposes LocDiff, a latent diffusion model for image geolocalization that diffuses over Spherical Harmonics Dirac Delta (SHDD) encodings of geolocations and decodes by mode-seeking, avoiding grids and galleries.
Problem
Image geolocalization on the global scale: grid-based and gallery-based methods lose spatial generalizability when test distributions do not match grid/gallery choices, while existing generative methods operate on raw coordinates lacking multi-scale information and suffer from manifold issues.
Approach
Encode spherical points as spherical harmonics coefficient vectors representing spherical Dirac delta functions, train a conditional SirenNet UNet DDPM in this latent space with a SHDD KL-divergence loss, and decode locations via learning-free mode-seeking over the sampled spherical distribution.
Key results
- LocDiff (L=47) reaches 53.3% at 200 km and 85.2% at 2500 km on Im2GPS3k, and the hybrid LocDiff-H reaches 15.3% at 1 km on Im2GPS3k, outperforming baselines at most scales.
- On OSV-5M, LocDiff (L=47) gets 11.0% at 25 km and 77.0% at 750 km, outperforming Diff R3, FM R3 and RFM S2 at those scales.
- When the gallery/grid is changed, GeoCLIP's 750 km accuracy on Im2GPS3k drops by up to 32% while LocDiff's changes by under 0.1%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Combine LocDiff candidate regions with GeoCLIP retrieval | LocDiff-H · Im2GPS3k and YFCC-26k | geolocalization accuracy across spatial scales: Im2GPS3k: 10.9 -> 15.3 (1 km), 53.3 -> 56.4 (200 km); YFCC-26k: 9.6 -> 13.2 (1 km), 37.5 -> 41.9 (200 km) | Helped |
| Combine LocDiff candidate regions with GeoCLIP retrieval | LocDiff-H · GWS15k | 1 km accuracy: 2.1 -> 0.9 | Hurt |
| Increase SHDD degree L (ablation) | LocDiff · Im2GPS3k | accuracy at 25 km, 200 km, and 1 km scales | Mixed |
| Use SHDD encoding and decoding instead of an RBF encoder with neural decoder (ablation) | LocDiff · Im2GPS3k | accuracy: 0.0 -> 10.9 (1 km); 0.0 -> 34.0 (25 km); 18.2 -> 53.3 (200 km) | Helped |
| Use SHDD encoding and decoding instead of Sphere2Vec with neural decoder (ablation) | LocDiff · Im2GPS3k | accuracy: 0.0 -> 10.9 (1 km); 0.0 -> 34.0 (25 km); 22.1 -> 53.3 (200 km) | Helped |
| Add small Gaussian noise to location encodings (ablation) | SHDD, RBF, and Sphere2Vec encoders · Location encoding perturbation | perturbation drift: 102.4 km; 89.1 km; 5.3 km | Mixed |
| Train with SHDD KL-divergence instead of L1 loss (ablation) | LocDiff · Im2GPS3k | accuracy: 0.0 -> 10.9 (1 km); 0.5 -> 34.0 (25 km); 20.3 -> 53.3 (200 km) | Helped |
| Train with SHDD KL-divergence instead of L2 loss (ablation) | LocDiff · Im2GPS3k | accuracy: 0.0 -> 10.9 (1 km); 0.7 -> 34.0 (25 km); 20.1 -> 53.3 (200 km) | Helped |
| Train with SHDD KL-divergence instead of cosine loss (ablation) | LocDiff · Im2GPS3k | accuracy: 7.5 -> 10.9 (1 km); 32.2 -> 34.0 (25 km); 53.0 -> 53.3 (200 km); 71.5 -> 72.5 (750 km); 84.9 -> 85.2 (2500 km) | Mixed |
| Reduce CS-UNet bottleneck width from w=128 to w=32 (ablation) | LocDiff, L=31 · Im2GPS3k | accuracy: 4.7 -> 5.1 (1 km); 27.0 -> 27.2 (25 km); 50.2 -> 50.9 (200 km); 70.8 -> 71.2 (750 km); 84.3 -> 84.1 (2500 km) | Mixed |
| Use MP16 gallery instead of grid anchors (ablation) | LocDiff · GWS15k | 1 km accuracy: 0.01 -> 0.57 (1M anchors); 0.07 -> 0.57 (500k anchors) | Helped |
| Replace MP16 gallery with grid points (ablation) | GeoCLIP · GWS15k | 2500 km accuracy: 83.82 -> 75.34 (1M grid); 83.82 -> 64.33 (21k grid) | Hurt |
Surprising findings
- Decoding with a learned neural decoder over location encodings (rbf, Sphere2Vec) performs far worse than the learning-free SHDD decoder, with 0% accuracy at 25 km.
- Cosine loss performs comparably to the SHDD KL-divergence at larger scales.
Limitations
- Numerical instability at high degree L beyond 47 limits spatial resolution; dimension grows quadratically with L.
- Fine-scale (1 km) accuracy of pure LocDiff remains low, requiring the GeoCLIP hybrid to be competitive.
- LocDiff-H underperforms LocDiff on GWS15k because the GeoCLIP gallery bias does not match that distribution.
Experimental setup
Datasets: MP16 Im2GPS3k YFCC-26k GWS15k OSV-5M YFCC-4k
Benchmarks: Im2GPS3k YFCC-26k GWS15k OSV-5M YFCC-4k
Metrics: accuracy at 1 km 25 km 200 km 750 km 2500 km
Baselines: [L]kNN PlaNet CPlaNet ISNs Translocator GeoDecoder GeoCLIP PIGEON Diff R3 FM R3 RFM S2 vMF
Builds on: DDPM Sphere2Vec SirenNet GeoCLIP RFM S2
Closest papers by meaning
- Around the World in 80 Timesteps: A Generative Approach to Global Visual Geolocation (CVPR 2025 · similarity 0.88)
- PIGEON: Predicting Image Geolocations (CVPR 2024 · similarity 0.86)
- GeoRanker: Distance-Aware Ranking for Worldwide Image Geolocalization (NeurIPS 2025 · similarity 0.85)
- Scaling Image Geo-Localization to Continent Level (NeurIPS 2025 · similarity 0.85)
- G3: An Effective and Adaptive Framework for Worldwide Geolocalization Using Large Multi-Modality Models (NeurIPS 2024 · similarity 0.85)
- Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks (ICLR 2024 · similarity 0.85)
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