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

Authors: Zhangyu Wang, Jielu Zhang, Zhongliang Zhou, Qian Cao, Nemin Wu, Zeping Liu, Lan Mu, Yang Song, Yiqun Xie, Ni Lao, Gengchen Mai
Primary area: applications to computer vision, audio, language, and other modalities
Keywords: Image geo-localization, location encoding, diffusion

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. The geolocalization accuracy of these methods is constrained by the choice of geographic grid cell sizes or the spatial distributions of the retrieval image/geolocation gallery, and
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 models to achieve image geolocalization with arbitrary resolutions. 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 to address the image geolocalization problem. We evaluate our LocDiffusion model against SOTA image geolocalization baselines. LocDiffusion achieves competitive geolocalization performance and demonstrates significantly stronger generalizability to unseen geolocations.

Decision: reject
Reviewer scores: 6, 3, 8, 3, 6

Reviews and discussion:
<thread>
creation date:
1730334777387

thread_type:
official_review

<thread_object>
creator: reviewer_s6yx

<content>
summary:
"This paper proposes a novel spherical positional encoding-decoding scheme to address non-linearity issues, enabling effective optimization and training for geolocation tasks within a diffusion-based model. Additionally, it introduces a new conditional latent diffusion model, LocDiffusion, which achieves state-of-the-art performance in image geolocalization."

strengths:
1. This paper introduces a noveldiffusion model to tackle the image geolocalization task, potentially benefiting the field and inspiring new directions.
2. The paper presents a new, learning-free encoder-decoder framework, mathematically demonstrating its robustness against sparsity issues in encoding space. This approach may also be beneficial for other remote sensing or geographical applications.
3. The paper provides solid mathematical proofs to support the properties it aims to achieve, particularly addressing issues of non-linearity and sparsity
4. The proposed approach achieves state-of-the-art results at the Region, Country, and Continent levels.
5. The paper is clear and well-written.

weaknesses:
1. The ablation study lacks sufficient detail. For instance, it would be helpful to see an ablation on SHDD encoding and decoding—how much improvement does it provide over positional encoding or other encoder-decoder methods? Additionally, is the KL loss significantly more effective than L1 or L2 loss? Further clarification on the contributions of the other proposed modules would strengthen the analysis.

2. The model's performance at the street and city levels is relatively weak and does not achieve competitive results.

3. This method requires huge computational cost, limited to the upbound of L.

4. Need more details about computational cost, training time and inference time.

questions:
1. In line 321, I noticed that $e_{lm}$ is used, but I couldn’t find a clear definition of it. Is $e_{lm}$ calculated from $F$? Could you clarify this or give the formula?

2. Is it reasonable to interpret the non-linear mapping between the locational embedding and position encoding space in Figure 1 as evidence of SHDD encoding’s superiority over traditional positional encoding? For my perspective, it is unconvincing, as the diffusion model introduces a non-linear mapping between $e$ and the image feature". Can you give more explanation about my confusion?
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<thread>
creation date:
1730644887913

thread_type:
official_review

<thread_object>
creator: reviewer_x6vd

<content>
summary:
This work proposes a diffusion model for image geolocalization (given an image, estimate where in the world the photograph was taken). Most work in this domain is based on either classification (partitioning the world into bins) or image retrieval. The main claim is that it overcomes limitations in spatial resolution caused by the partitioning scheme or the spatial distribution of gallery images. An encoding space is proposed that enables diffusion modeling on the sphere with the goal of reducing artifacts caused by modeling the sphere as a linear space.

strengths:
- It's interesting to consider alternative formulations of long-standing problems.
- The proposed approach seems to work well for low-resolution localization.

weaknesses:
- The work fails to deliver on its promise of eliminating the spatial resolution issues of previous approaches. Notably, Table 1 shows that it does not outperform approaches from 2016/2017 for low-error thresholds. The challenge is the computational complexity and memory consumption of the proposed approach. While promising, I'd need to see solid evidence that it improves relative to more straightforward approaches.

- L282 seems to be the crux of the problem with this approach, the assumption that the space is infinite. In practical implementations this is truncated, but it's unclear that this space is then the optimal space for the task. Existing approaches allow more data-driven specification of the space (for example, choosing spatial partitioning based on the distribution of the training dataset or implicitly based on the distribution of the gallery).

- L509 makes the claim that retrieval approaches depend heavily on the quality of the gallery, and seems to frame this as a negative. This is similar to saying, "the problem with the ImageNet dataset is that it requires so many images to represent the classes". Of course that's true; we always would love to use fewer images, but it's unclear how the proposed approach overcomes this issue. It still needs a large training dataset to fit the target function and these training images can serve as gallery images. There's clearly a negative to a large gallery, but in practice, it's easy to create indexes across billions of image embeddings using existing libraries. This scales well for practical uses.

- Some previous works have proposed strategies for overcoming the resolution limitations imposed by binning and a small gallery. This includes kernel density estimation in Revisiting IM2GPS in the Deep Learning Era by Nam Vo et al. A more complete assessment of previous attempts at addressing this issue should be included and an evaluation of simpler strategies should be included. Those missing baselines would likely be simpler to implement and might not suffer from the same memory challenges.

- Important related work is missing from CVPR 2024: "PIGEON: Predicting Image Geolocations" by Haas et al. This work proposes a hybrid of classification and retrieval which outperforms the results shown in Table 1 across the board. It notably does not generate poor results for low-error thresholds (which are the settings that most use cases require).

questions:
I don't have any particular questions, but would be happy to hear discussion regarding the weaknesses identified above.

The writing style made the key contributions and approach difficult to follow. This is a matter of personal style, but here are a few notes / suggestions from my reading of the work:
  - There's quite a bit of mathematical development that seems to obscure the contribution. For example, I found myself skipping over Section 4.1 because it felt like it was being overly mathy without any strong motivation.
  - I'd suggest for a future submission that the authors consider bringing Figure 2 to the forefront and emphasizing the high-level implementation before delving into the detailed mathematics.
  - Figure 1 has the longest caption I've ever seen in a CV/AI/ML paper. Many of those details would have been better presented after the high-level algorithm was clear as opposed to so early in the paper.
  - I find the heavy use of footnotes to be a bad sign for the writing of a paper. It indicates to me that some concepts are being presented out of place.
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</thread>
<thread>
creation date:
1730652499067

thread_type:
official_review

<thread_object>
creator: reviewer_u6sy

<content>
summary:
This paper tries to address the task of image geolocalization that estimates the geographic location where an image was taken. This paper introduces LocDiffusion, a novel generative approach to image geolocalization that leverages diffusion models to predict locations on Earth from images. The key innovation is a new Spherical Harmonics Dirac Delta (SHDD) encoding-decoding framework that enables diffusion in a Hilbert space while preserving spherical geometry. The authors also propose a Conditional Siren-UNet architecture for learning the conditional backward diffusion process.

strengths:
1.	Creative solution to the manifold projection problem in diffusion models.
2.	Novel SHDD encoding framework that handles spherical geometry.
3.	While the concept of KL-divergence itself is not new, the authors' specific application of it to spherical location generation through SHDD encoding and decoding appears to novel.
4.	The proposed Spherical Harmonics Dirac Delta (SHDD) encoding-decoding framework tackles the challenges of traditional image geo-localization methods by enabling the use of diffusion models for generating locations on the spherical surface of the Earth.

weaknesses:
1.	Quadratic scaling of SHDD encoding dimension may limit practical resolution.
2.	High space complexity and long training process.
3.	No ablation study.

questions:
1.	The main purpose of image-based geo-localization is to predict the location of an image. Unlike image retrieval-based localization, can this method predicate the coordinates? 
2.	Unlike using a large model for geo-localization, large model in general (even CLIP), has powerful prior knowledge, and therefore can discern the approximate location when the landmark is given. However, it just only predicts approximate locations, not coordinates. To build such a geographic knowledge base, a huge number of images are needed.
3.	I noticed some tricks in preventing overfitting phenomena, such as a very high dropout rate. Please analyze the overfitting of the proposed method.
4.	the advantages of the SHDD representation are primarily presented at a theoretical level, with limited experimental evidence to fully support the claims, without more experiments or analysis. By the way, there are only three tables in the entire paper, and one of them is still or just an experimental setup. There is no experimental-level evidence of the advantages of model and only a minor improvement in the main experiment.
5.	As shown in Table 1, in YFCC-26k, GeoDecoder has better performance than GeoCLIP in City 25km. I would recommend labeling the strong petitory and marking the improvement over them. Why is the performance so defective in 1km and 25km? The increase in generalization ability is built at the expense of model accuracy, which is hard to accept. I understand the need for generalization ability for this task, but I can only assume that for the previous models are flawed in solving the fitting problem. If the main purpose of this paper is in addressing the generalization ability, it would be more appropriate to analyze this aspect or collect an open-world test set to validate the model.
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<thread>
creation date:
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thread_type:
official_review

<thread_object>
creator: reviewer_be4r

<content>
summary:
1. Authors proposed a spherical positional encoding-decoding framework, which encodes points on a spherical surface into a Hilbert space of Spherical Harmonics coefficients.

2. Authors proposed a UNet architecture to learn conditional diffusion by minimizing a latent KL-divergence loss and train a LocDiffusion model that addresses the image geolocalization task via generation.

strengths:
S1: This article is well-written and easy to understand.

S2: This paper is the first work (to my knowledge) to use a diffusion model for image geolocalization.

(I also suggest that the authors change the word "generative" in the relevant claims to "diffusion ".)

weaknesses:
W1: This paper has a lot of descriptions of methods, but the experiments are insufficient to support the discussion of the methods. The authors need more ablation experiments. (I can revise the scores based on feedback from the authors.)

W2: Authors have a strong theoretical basis for the design of the method, but unfortunately, the experimental results are not significantly improved, whether it is GeoCLIP compared in the paper or PIGEON, which is not cited.

@InProceedings{Haas_2024_CVPR,
    author    = {Haas, Lukas and Skreta, Michal and Alberti, Silas and Finn, Chelsea},
    title     = {PIGEON: Predicting Image Geolocations},
    booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
    month     = {June},
    year      = {2024},
    pages     = {12893-12902}
}

questions:
Q1: Can you perform qualitative or quantitative experiments comparing the proposed positional encoding with other methods in the supplementary material?

Q2: Can you provide some ablation experiments?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730765697621

thread_type:
official_review

<thread_object>
creator: reviewer_gnes

<content>
summary:
This paper introduces a latent diffusion model called LocDiffusion for image geolocalization, aiming to predict precise geolocation on Earth from images with arbitrary resolutions. It proposes a novel spherical position encoding method, Spherical Harmonics Dirac Delta (SHDD) Representation, which encodes geocoordinates on Earth's spherical surface into a Hilbert space of Spherical Harmonics coefficients. The model then decodes these geolocations via a mode-seeking approach. A SirenNet-based architecture is used to learn the conditional backward process in the latent SHDD space by minimizing a latent KL-divergence loss. Experiments are conducted on the Im2GPS3k and YFCC-26k datasets, with comparisons to state-of-the-art methods like GeoCLIP.

strengths:
1. This work is the first generative model addressing the image geolocalization problem, offering a fresh perspective to the field.
2. The design of the Spherical Harmonics Dirac Delta (SHDD) Representation is innovative and tailored to the geocoordinate system, which is both novel and meaningful.
3. The paper is well-written and generally easy to follow.

weaknesses:
1. The performance gains over state-of-the-art methods, particularly GeoCLIP, are not well demonstrated. In Table 1, the proposed method achieves the best results in 5 out of 10 categories across two benchmarks, but the improvements are marginal, with differences of less than 0.5. Additionally, the method significantly underperforms in key categories like Street, City, and Region, raising concerns about its robustness across different geolocalization tasks.
2. The paper lacks a detailed analysis of computational efficiency, particularly in terms of training and inference speed, compared to existing methods. Since this is the first application of a diffusion model for geolocalization, it is important to understand how it compares to more established models, such as CLIP-based approaches, in terms of scalability and practicality for real-world applications. This could also helping assessing its potential impact and usability.

questions:
1. In Lines 92-93: The paper states, "Performing diffusion on the XYZ coordinates will likely lead to a point that is not on the spherical surface." Can the authors please provide further explanation or supporting evidence for this claim?
2. In Table 1, the method appears to struggle when the distance is below 1/3 or 1/10 of the spatial threshold in the SHDD representations. Could the authors explain why this occurs, especially given the claim that the model works for images with arbitrary resolutions? Does this limitation suggest the model is better suited for coarse-level geolocalization rather than fine-grained predictions?
3. Increasing the parameter $L$ seems to have a significant impact on performance. Could the authors provide more details on the computational resources required as $L$ increases? Understanding the trade-offs between computational cost and performance would offer useful insights into the model's scalability.
</content>
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<thread>
creation date:
1732791649406

thread_type:
official_comment

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creator: authors

<content>
title:
General Response 1. Improving the performance of LocDiffusion

comment:
**General Response 1. Improving the performance of LocDiffusion**

As all the reviewers have noticed and brought up in the comments, the performance of LocDiffusion compared with existing retrieval-based methods such as GeoCLIP and PIGEON was not ideal, especially on low-error scales such as 1km and 25km. We were also aware of this and managed to improve it to be on pare with or even outperform SOTA methods. Please see our updated Table 1 in the revised PDF.

The major factor that constrained the performance of LocDiffusion in the previous experiment results is the Legendre polynomial degree $L$. As we have discussed in Section 4.2 and Appendix A.3, the spatial resolution of SHDD decoding, i.e., the variance of SHDD decoding introduced by using a truncated spherical harmonics vector, is dependent on $L$. See Figure 3 in Appendix A.3 for an illustration. In our previous experiment results, while we were aware that larger $L$ brings better performance (See Figure 4(a) in  Appendix A.3), we only used $L = 31$ (i.e., SHDD encoding dimension = 1024) due to limited computational resources. The spatial resolution is around 320km. It is therefore very difficult to achieve high performance on fine-grained scales such as 1km and 25km because the intrinsic variance of the decoded locations is much larger.

To overcome this, we developed a dimension reduction technique to effectively use larger $L$. Briefly speaking, we find that not all $(L+1)^2$ dimensions are equally important in the computation of KL-divergence and in the decoding. See Figure 4(b) in Appendix A.3 for an illustration. Just like in signal processing, the Fourier features that have very small magnitudes can be discarded by a low-pass filter without significantly changing the shape of the signal; we applied the similar idea to the SHDD encoding. For example $L=47$ correspond to a 2403-dimensional vector, and we only kept the 1024 dimensions whose spherical Harmonics terms have top absolute coefficient values. In this way we were able to increase the spatial resolution of LocDiffusion and achieve further performance improvements.

However, further increasing $L$ leads to numerical instabilities because the coefficient values get too large and overflow when we calculate their exponentials for probability computation. As shown in Figure 4(b) in Appendix A.3, 2500 is the rough upper-bound of $L$ where we can stably compute the KL-divergence loss and decode an SHDD encoding. Therefore we stopped at 2403 dimensions. Whether we can overcome this hurdle and use even higher spatial resolutions is an interesting future research problem. However, the spatial resolution of $L=47$ is around 200 km, which is still significantly larger than 1km and 25km. Thus, while the performance of LocDiffusion on these two scales is close to GeoCLIP but can not beat it yet. 

Given the success of PIGEON (which is a hierarchical geolocalization framework), we explore combining LocDiffusion and GeoCLIP: since LocDiffusion is a generative model and outperforms GeoCLIP on coarser scales (> 200 km) while GeoCLIP outperforms on finer scales (<25km), we can use it as the first stage of geolocalization hierarchically. First, we sample multiple times (e.g., 16) and get a rough distribution of candidate locations, i.e. they indicate where the true answer is highly likely to reside. Then, we restrict the retrieval of GeoCLIP to the neighborhoods (200 km radius) of these candidate locations. We find that this simple combination yields better results than both GeoCLIP and LocDiffusion used alone. This approach is to  recommendation systems' retrieve and rerank approach. This combination points to interesting future work, too, and we wish to demonstrate that **our generative approach is not meant to beat and replace retrieval-based models; instead, they have their respective advantages and the best strategy is to fuse them into one system**.
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<thread>
creation date:
1732791995248

thread_type:
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creator: authors

<content>
title:
General Response 2. Clarification on the contribution of the paper

comment:
**General Response 2. Clarification on the contribution of the paper**

Our goal in this research is not to beat and replace retrieval/classification based models; instead, we wish to provide a **more spatially generalizable alternative** and align it with previous works that try to overcome the resolution limitations of bins and galleries. More importantly, apart from the specific application to geolocalization, the design of SHDD encoding/decoding techniques itself may open up research opportunities in other applications where decoding locations is required (as far as we know, it is the first deterministic, learning-free spherical location decoding method).

Here we demonstrate that 1) how existing approaches rely on co-locations between training and testing data and why it may be problematic, 2) how our approach does not suffer from this problem (as demonstrated in Table 2 and Appendix A.4) and 3) by hierarchically using our model as the first stage of retrieval we can improve SOTA approaches (e.g., GeoCLIP) at all scales.

First, we'd like to illustrate that the existing retrieval process used by GeoCLIP (as in Table 1) implicitly relies on a strong assumption that many test images co-locate with the retrieval gallery. To demonstrate, we take the MP16 gallery used by GeoCLIP and compare the locations in the gallery with the locations in the Im2GPS3K test set. We measure how closely test locations align with the gallery locations by counting the number of gallery locations that are within 1km/25km from a given test location. There are 63.5% test locations that can find at least one location in the MP16 gallery that is less than 1 km away, and 95.2% less than 25 km away. **This means the “correct answer” is almost always present in the gallery – this is a very strong spatial inductive bias**. If we do not have access to such a gallery, for example if we use a set of evenly spaced locations on Earth as the gallery, the two numbers drop to 0.1% 1km away and 38.9% 25 km away, respectively. A detailed analysis can be found in Appendix A.4. This can be very problematic since **in real-world settings, such a well-aligned gallery is hard to obtain**. GWS15K is an actual example. In the GeoCLIP paper, the low-error resolution performance on GWS15K is significantly worse (0.6 on 1km, 3.1 on 25km) than on Im2GPS3K (14.11 on 1km, 34.47 on 25km). However, both GeoCLIP and PIGEON did not publicize this dataset, and to construct it using Google APIs takes longer time beyond the rebuttal period. We are happy to include this result in the camera-ready version if this paper gets accepted.

Second, we’d like to explain why our LocDiffusion model does not have this issue. SHDD encoding is an implicit representation of a **continuous function**. One can **exactly** evaluate the function values at any point on the sphere without the need of any gallery or spatial bins; the only factor that restricts the accuracy of the evaluation is the computational setting (i.e., using how many digits of floats). Instead, retrieval-based methods can only be applied to locations that exist in the gallery. In this sense, our claim in the paper that our method can achieve **arbitrary spatial resolution** can be confusing comparing to the **spatial resolution of SHDD decoding** we discussed in General Response 1. We sincerely apologize for the overload of concepts and we will replace the “arbitrary spatial resolution” term with “can be evaluated at arbitrary locations”. The benefit of being independent of a pre-defined gallery is stronger spatial generalization. Table 2 in the main paper and Figure 5 in Appendix A.4 clearly demonstrate that LocDiffusion performs stably well no matter whether the SHDD decoding is evaluated on MP16 gallery points or on evenly distributed grid points.

Finally, as we have also discussed in General Response. 1, **the best strategy may be a hierarchical combination of real-valued diffusion and discrete retrieval/classification (like that of PIGEON): ** use diffusion in coarser scales (>200km) to accurately narrow down the region the image may locate and for further fine scales (< 25km) use a locally trained retrieval model. This will help avoid retrieving from an extremely large gallery that might introduce noise retrieval results because of the needs to be both global and spatially fine-grained. The performance gain of such a combination is presented in the updated Table 1.
</content>
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creation date:
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thread_type:
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creator: authors

<content>
title:
General Response 3. Addressing the quadratic complexity of SHDD encoding

comment:
**General Response 3. Addressing the quadratic complexity of SHDD encoding**

The Legendre polynomial degree $L$ controls the sizes of spherical harmonics wavelengths and has a significant impact on the resolution (See Figure 4(a) in Appendix A.3). Several reviewers are rightfully concerned that the dimension of SHDD encoding scales quadratically. We developed a low-pass filtering technique to effectively reduce the dimensionality.

Briefly speaking, we find that not all $(L+1)^2$ dimensions are equally important in the computation of KL-divergence and in the decoding. See Figure 4(b) in Appendix A.3 for an illustration. Just like in signal processing, the Fourier features that have very small magnitudes can be discarded by a low-pass filter without significantly changing the shape of the signal; we applied the similar thing to the SHDD encoding. We used $L=47$, got a 2403-dimensional vector, and only kept the 1024 dimensions whose spherical Harmonics terms have top absolute coefficient values. In this way we were able to increase the spatial resolution of LocDiffusion and saw significant performance improvements especially for scale 1km and 25km.

Another possible approach is analogous to nested dropout. For each pass we only evaluate a fixed-size random subset of all the dimensions in hope that as training epochs increase, all dimensions are visited and learned.
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creation date:
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creator: authors

<content>
title:
General Response 4. Computational complexity

comment:
**General Response 4. Computational complexity**

The computational complexity of LocDiffusion, like most diffusion models, lies mainly in the diffusion process. **The SHDD encoding/decoding is deterministic and learning-free, which is very fast**. In fact, if the training data are fixed, we only need to construct a look-up table. Therefore, the time complexity of LocDiffusion is at the same level as the specific diffusion model we employ (for example, in this paper we used the classic DDPM model without sampling acceleration). We potentially can apply more efficient diffusion approaches such as stable diffusion or consistency diffusion.

The space complexity depends on the input and output dimensions of the diffusion model, i.e., the dimensions of SHDD encodings. As we have discussed in General Response 1 and General Response 3, it is both possible to reduce the dimensionality of SHDD encodings by low-pass filtering, and recommended not to use very high dimensional SHDD encodings for the sake of computational stability. 

For details on the training and inference time/space costs, please see Appendix A.5. The inference time of LocDiffusion is about 0.05s per query on a single NVIDIA RTX5500 24G GPU, while GeoCLIP about 0.02s. Therefore in practice, the computational complexity of LocDiffusion should not be a huge concern. If we need to scale up, we can apply the well-established sampling acceleration techniques developed for diffusion models.
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<thread>
creation date:
1732792442364

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creator: authors

<content>
title:
General Response 5. Ablation studies

comment:
**General Response 5. Ablation studies**
In Appendix A.6 we have added more ablation experiments to help understand the behavior of the proposed model. 
There are three sets of ablation experiments:

**(1) Ablation on replacing SHDD with other location encoding/decoding methods**

Theoretically we argued in Section 4.1 that existing location encoding methods suffer from sparsity and non-linearity so that they are not suitable for location decoding. This is supported by ablation studies. Please see Table 6 and Table 7 in Appendix A.6. To summarize, we replace SHDD encoder/decoder with two commonly used location encoders (rbf and Sphere2Vec) and train a neural network to decode the diffusion output back to locations. After the replacement, the geolocalization performance is reduced by half on coarser scales, and on finer scales (1km and 25km) the accuracy drops to 0. We further demonstrate that such performance drop comes partially from the non-linearity of these location encodings (another reason is that the neural decoder is not 100% accurate). Adding a small Gaussian noise (variance = 0.01) to a non-SHDD location encoding, the spatial drift of the decoded location can be as large as 102.4km (rbf) and 89.1km (Sphere2Vec), while for SHDD encoding this drift is 5.3km. That means, in the case that the diffusion generated output is not noiseless (which is almost certain), SHDD suffers less.

**(2) Ablation on replacing SHDD KL-divergence loss with other losses**

We try to train LocDiffusion with alternative losses, such as L1/L2 and cosine distance loss. Please see Table 8 in Appendix A.6. The findings are very interesting: L1/L2 losses are much worse than SHDD KL-divergence, whereas cosine distance loss yields fairly good results on coarser scales. Our hypothesis is that the cosine distance loss is mathematically similar to the SHDD KL-divergence loss (SHDD KL-divergence is the sum of exponential element-wise multiplications, while cosine similarity is the sum of raw element-wise multiplications; the difference is that exponential terms are non-negative and the probability mass is more concentrated, i.e., it should be better than cosine losses on fine-grained scales, but not very different on coarser scales). This may indicate that we can use cosine loss as a computationally friendly alternative as long as we do not insist on high performance on low-error scales. This is also an interesting future work.

**(3) Ablation on CS-UNet modules**

We have explored many alternatives of the CS-UNet architecture, but unfortunately we did not record them for ablation studies. Due to the limited time given for rebuttal and the long training time and various combinations of alternative modules, we have not been able to conduct a very thorough ablation study on this part. But according to our experience, one of the most important factors is the bottleneck dimension of the CS-UNet: shrinking the bottleneck width w of the CS-UNet seems to help alleviate model overfitting (we can adopt a lower dropout rate) and slightly boost performance, but it makes the model more difficult to train. We managed to do this experiment and reported the results in Table 9 in Appendix A.6.
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Metareview:
metareview:
The submission proposes LocDiffusion, a novel latent diffusion model for image geolocalization, leveraging a spherical positional encoding-decoding scheme (SHDD) to operate in a Hilbert space while preserving Earth's spherical geometry. While the paper presents innovative ideas and introduces a new generative framework for geolocalization, its contributions are undermined by limited experimental improvements, incomplete comparisons to related work, and unresolved concerns raised by reviewers during the discussion period.

Reviewers GNES, Be4r, and X6VD expressed concerns about whether the proposed approach offers tangible benefits over existing methods in terms of accuracy and practical usability. Missing or insufficiently analyzed baselines include well-established methods like PIGEON (CVPR 2024) and other retrieval-based geolocalization approaches. Reviewer X6VD highlighted these omissions as critical weaknesses, questioning the significance of the proposed contributions. The authors’ response addressed some writing concerns but failed to adequately clarify key methodological aspects, as noted by Reviewer S6YX.