scMRDR: A scalable and flexible framework for unpaired single-cell multi-omics data integration

Thank you for your thoughtful review and for highlighting the strengths of our work, including the paper's clarity, the effective integration of key techniques into a scalable framework, and the novelty of beta-VAE for disentanglement and isometric loss in preserving biological structure. We also appreciate your recognition of our rigorous evaluation across multiple integration scenarios. We appreciate your feedback and believe the concerns raised—regarding novelty, baseline comparisons, and evaluation—stem from some misunderstandings that we can clearly address in our response.

1. Novelty compared to other disentanglement methods

Although there have been some previous methods that decouple the latent space, they are still limited to the integration of two modalities (such as contrastive learning) or require the use of partial paired information.

• scTFBridge uses a disentangled hierarchical VAE but requires fully paired data for training and is restricted to dual-modality integration (due to contrastive learning).
• scMaui leverages variational product-of-experts autoencoders and adversarial learning, but also limits in paired data.
• InClust+ employs a mask-enhanced VAE with stacked modules to integrate multimodal data. Although it can achieve integration of unpaired multi-omics data, this still requires separate processing between each pair of datasets.

In contrast, the innovation of our method lies in：

• Instead of distinguishing data from different modalities at the input stage, we treat them equally as a single sample, and directly leveraging beta-VAE for disentanglement, which allows us to avoid limitations in scalability and flexibility imposed by designs such as partial paired information supervision, stacked encoders, and cross-modal contrastive learning, and therefore, it is conveniently adaptable to the integration of completely unpaired data across multiple omics.
• As you pointed out, to ensure that the disentangled representations retain meaningful biological heterogeneity, we first and innovatively introduced an isometric regularization. Adversarial loss and mask loss have indeed appeared in previous articles, but their combination in this paper is not merely a simple engineering trick. Instead, it is an integral part of our novel framework, which is designed to accommodate the concatenation of all modal data and the unified use of a single beta-VAE to learn disentangled and meaningful representations, rooted in the theory of disentangled representation learning.
• Theoratically, without additional constraints, such a disentangled subspaces are unidentifiable (i.e., not unique) [1]. We leverage this unidentifiability and, by imposing isometric and adversarial regularization, constrain the modality-shared subspace to be the one that preserves the maximum sample structure information from the original latent space while aligning different modalities, thereby endowing the unified embedding with biological significance.

2. GLUE's performance in section 4.3

The comparative method GLUE demonstrates good performance in Sections 4.2 and 4.4, but is significantly lower in Section 4.3. This is because:

• Scaled metrics: We initially displayed all metrics after min-max scaling (scIB's default setting), which resulted in the lowest values being scaled to 0. In fact, the raw metric values are not abnormally low (Table 2 in Appendix). We recognize that this presentation method could lead to widespread misunderstandings and will present the original values of each metric in the revised main text.
• Preprocessing methods: GLUE recommends using LSI for the preprocessing of scATAC, but the function scglue.data.lsi provided by the GLUE fails to deal with the scale of 54,844 cells (keep returning NaN values). Therefore, in the initial version of the paper, we substituted PCA (the preprocessing method for scRNA in GLUE), which resulted in a significant drop in model performance. We now used the LSI method for large-scale sparse data in sklearn TruncatedSVD, and there's a significant improvement in GLUE's performance, though it still falls short of our method. This highlights another advantage of our method: it does not rely on any preprocessing methods.
• Besides, as you suggested, we conducted sensitivity analysis for GLUE: we compare the performance of GLUE under 8 settings: preprocessing methods (LSI / PCA) x modeling layers (Negative Binomial for raw counts / Normal for normalized expressions) x whether to use highly variables genes. All configurations of GLUE performs worse than our method.

Sensitivity analysis of GLUE in large-scale two-omics integration

3. raw scIB metrics

We apologize for the widespread misunderstanding caused by our previous presentation.

• For convenience in calculating the summary metrics, we used scIB's default settings (we cited scIB in line 197-198), which involved min-max scaling each metric to 0-1 before summing them up, and we directly visualized the scaled scores in the main text (We explained it in the captions of each figure)
• we attached the original unscaled metrics in the appendix (Table 2). We also mentioned that in the captions of Figures 4, 5, and 7.
• We recognize that this approach has led to widespread misunderstandings, particularly as scaling can further lower the values of some methods. Therefore, we are now updating to report unscaled metric values and aggregated scores based on unscaled values in the revised main text. (Please see the raw values in our response to Reviewer XHw7 due to space limitations)

4. totalVI as a baseline

As you pointed out, totalVI is an integration method for paired data (each cell are simultaneously measured in multiple omics), which is fundamentally different from the problem we want to address - integrating cells with single-modality measurements from different datasets (unpaired/diagonal integration). Therefore, we excluded it.

In paired integration, the integration method utilizes multi-omics features to obtain a latent embedding for each cell. Each multi-modal cell has only one embedding. In contrast, unpaired integration aims to align cells measured across various modalities from different datasets. Each cell in each modality will have its own embedding, required to preserve biological heterogeneity information in each modality while aligning the data across different modalities.

Relevant benchmarks [2-3] all distinguish the two scenarios and corresponding methods. Even assuming unpaired data as paired, totalVI cannot handle it (due to unequivalent sample sizes across modalities and it generating a single embedding for each pair).

5. downstream impact

• We added an additional downstream analysis: spatial location imputation of scRNA and scATAC.
• We integrated scRNA, scATAC, and spatial transcriptomics (merFISH) [4] data using our method, and then used the aligned latent representation to interpolate the missing spatial locations in single-cell data by optimal transport. Visualization shows that this interpolation performs well, where inferred locations of cells align well with the provided cortex layers annotations. We apologize that we are not allowed to include the figures here due to the rebuttal guidelines, but they will be presented in the revised version of the manuscript.
• Detecting spatial variable genes (SVGs): Due to low coverage of merFISH (only 254 genes), only 103 genes are detected as SVGs (SPARKX $P_{adj}<1e-20$). We leveraged the spatially interpolated scRNA data (26069 genes) and 4063 SVGs (SPARKX $P_{adj}<1e-20$) are detected. We replicated 85 out of 101 SVGs detectable by merFISH (such as Lamb5, Calb1, Cux2, etc.), and also revealed new SVGs (such as Sema5b, Gpr88, Zfhx4, etc.). These findings are also supported by some previous studies [5-6].
• Similarly, using scATAC with imputed spatial locations, we identified 386 SVGs on gene activity scores, including several key transcription factors (such as Zfhx4, Cux1, Cux2, Foxp1, etc.). This will further support the investigation of spatially specific regulatory mechanisms.
• This indicates that our integration method preserves the unique biological information of each cell and can be used to further impute missing spatial location information, thereby enabling more biological discoveries.

Reference:

[1] Khemakhem, et al. Variational autoencoders and nonlinear ica: A unifying framework. International conference on artificial intelligence and statistics (2020)

[2] Fu, S. et al. Benchmarking single-cell multi-modal data integrations. Nat Methods (2025)

[3] Chuxi X. et al. Benchmarking multi-omics integration algorithms across single-cell RNA and ATAC data, Brief in Bioinfo (2024)

[4] Zhang, M. et al. Spatially resolved cell atlas of the mouse primary motor cortex by MERFISH. Nature (2021).

[5] Stickels, R.R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with Slide-seqV2. Nat Biotechnology (2021).

[6] Liau, E.S. et al. Single-cell transcriptomic analysis reveals diversity within mammalian spinal motor neurons. Nat Commun (2023).

Thank you for your thoughtful feedback and for recognizing the improvements in evaluation clarity and the additional downstream analyses on spatial transcriptomics.

We would like to emphasize that the significance of our work lies in providing a convenient framework for integrating non-paired multi-omics data without relying on specific pairing information or conventional pairwise transfer. To achieve this, we established a framework with a unified encoder treating observation in different omics equally as a single sample (instead of stacked specific encoders) for disentangled learning for the first time. Further, we proposed a joint optimization goal, combining our novel use of isometric regularization with existing techniques, enabling our flexible framework effective. Experiments demonstrate its scalability in large sample size and over 2 omics. We agree your valuable suggestion and will clarify the theoretical motivation for regularized disentangled representations better in the revised manuscript.

Thank you for recognizing the strong motivation of our work on unpaired omics integration and for highlighting scMRDR's scalable approach and its very competitive performance across multiple metrics. We appreciate your acknowledgment of the method's effectiveness in both two-omics and triple-omics integration tasks. We appreciate your insightful questions and we believe the concerns have been well clarified below.

1. On the "atlas" scale

• We recognize that our experiment in section 4.3 (69,727 + 54,844 cells) does not truly qualify as atlas-level, which may require millions of cells; therefore, we will change the term "atlas-scale" to "large-scale" in the final version of the paper.
• Meanwhile, we believe this does not diminish the significance of our method, because
  • (a) as you pointed out, we demonstrated the scalability of our method through the integration of cells at the 100,000-cell level, while many comparative methods fail to achieve this;
  • (b) As shown in the latest benchmark article published on this month [1], many of the newly published methods over the past two years can still only perform integration on paried datasets (paired integration) or partial paired dataset (mosaic integration), while methods supporting complete unpaired data integration are still scarce (14 out of 40), especially for integrating completely unpaired data across more than two omics, which highlights the significance of our work for its capacities in completely unpaired (diagonal) integration with over two omics.

2. On the hyperparameters

Based on the original ablation experiments, we conducted experiments with a range of different hyperparameter combinations on the regular-scale two-omics dataset.

• The performance is consistently better than the ablation results when removing any individual component, and the worst model is the baseline without any regularization. While different hyperparameter combinations have a certain impact on performance, including trade-offs among various losses and the influence of randomness (isometry is more essential to bio-conservation while adversary more vital to modality alignment, but simply increasing the value of a certain parameter will not necessarily enhance the model's performance in a specific aspect), the results are generally robust to the choice of hyperparameters.
• Our design is not by chance. Theoratically, without additional constraints, such a disentangled subspaces are unidentifiable (i.e., not unique) [2]. We leverage this unidentifiability and, by imposing isometric and adversarial regularization, constrain the modality-shared subspace to be the one that preserves the maximum sample structure information from the original latent space while aligning different modalities, thereby endowing the unified embedding with biological significance.

Performance under different hyperparameter configurations

3. On the performance of scGLUE in section 4.3

We apologize for any misunderstandings caused by the previous presentation. In Section 4.3, the reasons for the lower metric values of GLUE include:

• Scaled metrics: We initially displayed all metrics after min-max scaling (scIB's default setting), which resulted in the lowest values being scaled to 0. In fact, the raw metric values are not abnormally low (Table 2 in Appendix). We recognize that this presentation method could lead to widespread misunderstandings and will present the original values of each metric in the revised main text.
• Preprocessing methods: GLUE recommends using LSI for the preprocessing of scATAC, but the function scglue.data.lsi provided by the GLUE fails to deal with the scale of 54,844 cells (keep returning NaN values). Therefore, in the initial version of the paper, we substituted PCA (the preprocessing method for scRNA in GLUE), which resulted in a significant drop in model performance. We now used the LSI method for large-scale sparse data in sklearn TruncatedSVD, and there's a significant improvement in GLUE's performance, though it still falls short of our method. This highlights another advantage of our method: it does not rely on any preprocessing methods.
• We conducted sensitivity analysis for GLUE: we compare the performance of GLUE under 8 settings: preprocessing methods (LSI / PCA) x modeling layers (Negative Binomial for raw counts / normal for normalized expressions) x whether to use highly variables genes. All configurations of GLUE performs worse than our method.

Performance of GLUE in large-scale two-omics integration

Reference

[1] Fu, S. et al. Benchmarking single-cell multi-modal data integrations. Nat Methods (2025)

[2] Khemakhem, et al. Variational autoencoders and nonlinear ica: A unifying framework. International conference on artificial intelligence and statistics (2020)

Thank you for your valuable feedback and for recognizing our work. As promised, we will present the unscaled metrics in the final version of the manuscript.

Thank you for your positive feedback on the clarity of our manuscript, the significance of the problem, and the performance of our method. We appreciate your insightful questions and we believe the concerns have been well clarified below.

1. Explantions on experimental results

• We previously visualized min-max scaled metrics in Fig.4,5,7: For convenience in calculating the summary metrics, we used scIB's default settings [1], which involved min-max scaling each metric to 0-1 before getting aggregate scores, and directly visualized the scaled scores in the main text (explained in the captions of each figure)
• we attached the original unscaled metrics in the appendix (Table 2). We also mentioned that in the captions of Figures 4, 5, and 7.
• We recognize that it has led to widespread misunderstandings. Therefore, we will turn to present unscaled metric values and aggregated scores based on unscaled values (see tables below)

2. Comparison with recently published methods

We referenced the newest benchmark paper published in Nature Methods this month [2], and added comparison with two new methods for unpaired multi-omics integration: MaxFuse [3] and SIMBA [4] (see tables below). Besides,

• in this latest benchmark, GLUE remains the best-performing method among all compared methods for regular-scale unpaired integration of scRNA and scATAC, indicating that our original benchmark is still meaningful;
• many of the newly published methods discussed in this benchmark can still only perform integration on paried datasets (paired integration) or partial paired dataset (mosaic integration), while methods supporting complete unpaired data integration are still scarce (14 out of 40), especially for integrating completely unpaired data across more than two omics. This further highlights the significance of our work.

performance on two-omics integration

Performance on large-scale two-omics integration

Performance on triple-omics integration

3. Clarifications of questions

• We used the modality-shared latent embeddings for UMAP visualization and subsequent analysis.
• abnormal metrics values: As explained before, we initially displayed all metrics after min-max scaling (default setting of scIB package), which scales the lowest values to 0. Though we explained it in the captions of each figure, we recognize that it leads to widespread misunderstandings, and we will present the raw values in the revised main text.
• We effectively capture biologically meaningful representations:
  • Our modality integration method demonstrates excellent bio-conservation: despite an unsupervised manner, different cell types are separated into distinct clusters, while the same cell type across different modalities cluster together in the UMAP visulaization.
  • Additional downstream analysis: We integrated scRNA, scATAC, and spatial transcriptomics (merFISH) using our method, and then used the aligned latent representation to interpolate the missing spatial locations in single-cell data by optimal transport. Visualization shows that this interpolation performs well, where inferred locations of cells align well with the provided cortex layers annotations. We apologize that we are not allowed to include the figures here due to the rebuttal guidelines, but they will be presented in the revised version of the manuscript.
  • Detecting spatial variable genes (SVGs): Due to the low coverage of merFISH (only 254 genes), only 103 genes are detected as SVGs (SPARKX $P_{adj}<1e-20$). We leveraged the spatially interpolated scRNA data (26069 genes) and 4063 SVGs (SPARKX $P_{adj}<1e-20$) are detected. We replicated 85 out of 101 SVGs detectable by merFISH (like Lamb5, Calb1, Cux2, etc.), and also revealed new SVGs (like Sema5b, Gpr88, Zfhx4, etc.), which are supported by some pervious studies [5-6].
  • Similarly, using scATAC with imputed spatial locations, we identified 386 SVGs in gene activity scores, including several key transcription factors like Zfhx4, Cux1, Cux2, Foxp1, etc. This will further support the investigation of spatially specific regulatory mechanisms.
  • This indicates that our integration method preserves the unique biological information of each cell and can be used to further impute missing spatial location information, thereby enabling more biological discoveries.
• Cell type labels in different omics has been aligned between different modalities. It should be emphasized that we did not use these labels during training (completely unsupervised); cell type labels were only used for evaluation.

Reference

[1] Luecken, M.D. et al. Benchmarking atlas-level data integration in single-cell genomics. Nat Methods (2022)

[2] Fu, S. et al. Benchmarking single-cell multi-modal data integrations. Nat Methods (2025)

[3] Chen, S. et al. Integration of spatial and single-cell data across modalities with weakly linked features. Nat Biotechnol (2024)

[4] Chen, H. et al. SIMBA: single-cell embedding along with features. Nat Methods (2024)

[5] Stickels, R.R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with Slide-seqV2. Nat Biotechnology (2021).

[6] Liau, E.S. et al. Single-cell transcriptomic analysis reveals diversity within mammalian spinal motor neurons. Nat Commun (2023).