scMRDR: A scalable and flexible framework for unpaired single-cell multi-omics data integration
Authors: Jianle Sun
Chaoqi Liang
Ran Wei
Peng Zheng
LEI BAI
Wanli Ouyang
Hongliang Yan
Peng Ye
Venue: NeurIPS 2025 spotlight ()
Keywords: Single-cell omics
Multi-omics integration
Unpaired data
Disentangled representation
Variational inference
Adversarial learning
Isometric regularization
Masked loss
Primary area: machine_learning_for_sciences

Abstract: Advances in single-cell sequencing have enabled high-resolution profiling of diverse molecular modalities, while integrating unpaired multi-omics single-cell data remains challenging. Existing approaches either rely on pair information or prior correspondences, or require computing a global pairwise coupling matrix, limiting their scalability and flexibility. In this paper, we introduce a scalable and flexible generative framework called single-cell Multi-omics Regularized Disentangled Representations (scMRDR) for unpaired multi-omics integration. Specifically, we disentangle each cell’s latent representations into modality-shared and modality-specific components using a well-designed $\beta$-VAE architecture, which are augmented with isometric regularization to preserve intra-omics biological heterogeneity, adversarial objective to encourage cross-modal alignment, and masked reconstruction loss strategy to address the issue of missing features across modalities. Our method achieves excellent performance on benchmark datasets in terms of batch correction, modality alignment, and biological signal preservation. Crucially, it scales effectively to large-scale datasets and supports integration of more than two omics, offering a powerful and flexible solution for large-scale multi-omics data integration and downstream biological discovery.

A Scalable and Flexible Framework for Unpaired Single-Cell Multi-Omics Data Integration
ScMRDR:
Jianle Sun 1.2, Chaoqi Liang', Ran Wei', Peng Zheng', Lei Bai', Wanli Ouyang', Hongliang Yan', Peng Ye .31
Shanghai Artificial Intelligence Laboratory. Carnegie Mellon University, The Chinese University of Hong Kong. Guangzhou Laboratory
Abstract
Advances in single-cell sequencing have enabled high-resolution profiling di- molecular modalities, while integrating unpaired multi-omics single-cell data remains challenging. Existing approaches either rely on pair information or prior correspondences, require computing global pairwise coupling matrix, limiting their scalability and flexibility. In this paper, we introduce scalable and flexible generative framework called single-cell Multi-omics Regularized Disen- tangled Representations (scMRDR) for unpaired multi-omics integration. Specifi- cally, we disentangle each cell's latent representations into modality-shared and modality-specifie components using a well-designed 3-VAE architecture, which are augmented with isometric regularization to preserve intra-omics biological het- erogeneity. adversarial objective to encourage cross- modal alignment, and masked reconstruction loss strategy to address the issue of missing features across modali- ties. Our method achieves excellent performance on benchmark datasets in terms of batch correction, modality alignment, and biological signal preservation. Crucially, it scales effectively to large-scale datasets and supports integration of more than two omics, offering powerful and flexible solution for large-scale multi-omies data integration and downstream biological discovery.
Introduction
Recent advances in single-cell sequencing technologies have enabled the measurement of diverse molecular modalities at single-cell resolution, such gene expression (scRNA), chromatin acces- sibility (sCATAC), and protein abundance (scProtein). These complementary data sources offer a comprehensive view of cellular states and dynamics. Although a few protocols allow limited joint profiling using marker-based techniques, they still suffer from low feature coverage and reduced flexibility due to the destructive nature of single-cell assays, making it remain technically challenging to jointly measure multiple modalities within the same cell. Consequently, large-scale single-cell datasets are typically unpaired across different modalities [33]. This unpaired nature, coupled with significant technical noise such as batch effects, dropouts. and sequencing depth variation, makes data integration shared biologically meaningful latent space highly nontrivial task [27
The goal of multi-omics data integration is to map single-cell data in different omics into a shared latent space, where representations across modalities distributionally aligned while preserving biological differences between cell types and correcting for technical variations due to experimental batches (p). Existing approaches explored joint dimension reduction (Fig[p)), like factor
Corresponding author.
Source codes are available at httttp://ggthub. com/sjl coom/jjlljtt//eee sall-jjttsscRDDR Email Address: jianles@ @wwde@aannddddeeee.mm Work was done during an internship at Shanghai Al Laboratory.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Gene expression
Modality integration
Batch correction
Chromatin accessibility
Bio (cell type) conservation
Unified cell embeddings
Surface protein
Joint dimensionality coduction
aligoment
Disenlangied represeniatiion
Isometric loss
Adverstrial training
Paired
Distance
gruph
Paired inputs or prior comrspondence
Limited two omnics layers
Flexible pair needed
small datasets
Scalable to more omies layers and large datasets
Figure Method overview. (a) Multi-omiss data integration. The goal is to integrate single-cell data in different modalities into an aligned latent space while preserving biological information and correcting technical noise. (b) Integration via joint dimension reduction (e.g.. joint autoencoders). It typically works with paired data (measurements on different omics within the same cell). (c) Integration via manifold alignment between the geometric structures (e.g., KNN distance graphs) of different omics. It does not require paired data, but is typically limited to small-scale datasets involving only two omics modalities. (d) Our framework, based on disentangled representations, is flexible to completely unpaired data and scalable to large datasets with more than two omics.
analysis D. or deep generative models (24). However, they typically rely on paired partially paired data 2 6 to guide the integration, or require external prior knowledge [8] or pre-lcarned coupling matrix to bridge modalities, limiting their flexibility. On the other hand, some approaches
employ manifold alignment (T)) including optimal transport [1] 7 or unsupervised manifold transformation [ 39]. However, these methods, relying computing global pairwise coupling matrix, typically restrict to integrating two modalities, and encounter serious computational issues in large datasets due the complexity of inter-modal alignment, struggling in scalability.
To address the challenges, we proposed scalable flexible generative model named single-cell Multi-omics Regularized Disentangled Representations (scMRDR) integrate unpaired multi-omies single-cell data into unified latent space (Fig Id). Unlike existing methods, scMRDR requires neither paired samples and prior information establishing global correspondences across different modalities. Instead, we achieve the integration based on the disentanglement of each sample's latent code into shared and modality-speellee components via well-designed 3-VAE architecture, incorporating isometric regularization to ensure the conservation of biological information, and adversarial training to encourage the fusion of different modalities, with masked loss function to address the feature missing issue in different modalities (Fig
Due to the single unified encoder-decoder architecture, ScMRDR is flexible to completely unpaired data and able to scale to large datasets with more than two modalities naturally. Applied to real-world unpaired single-cell data, scMRDR demonstrates excellent performance in modality integration, batch correction as well as bio-conservation, surpassing a broad range existing methods. Moreover, scMRDR scales robustly to large datasets, and readily accommodates additional omics layers. These results collectively underscore scMRDR as a flexible and scalable framework for large-scale unpaired single-cell data integration and the discovery of complex biological mechanisms.
summarize contributions follows: (1) Through in-depth analysis of existing works in field of multi-omics integration, we identify their limitations in flexibility and scalability, and propose a generative framework with unified single encoder-decoder 3-VAB disentangle latent represen- tations; (2) We propose joint optimization goal, incorporating isometric regularization, adversarial

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training, and masked loss to facilitate modality fusion while preserving biological signals; (3) We validate scMRDR through extensive experiments on multiple real-world datasets, demonstrating its strong flexibility and scalability on large-scale datasets and more complex multi-omics integration tasks, as well as its practical significance in downstream biological analyses (such as spatial position imputation).
Related work
Integrating multi-omics data has been extensively studied, with methods typically falling into two broad categories. Joint dimension reduction methods, including statistical models such as factor analysis based method like MOFA M1. canonical correlation analysis (CCA)-based methods like Seurat v3 [30]. as well as deep generative models such as sc Vc-bsed (24) adaptations, assumne access to matched (paired) measurements across omics layers, enabling supervised or semi-supervised learning of joint representations. For example, MultiVI [2] integrates paired multi-omic data by directly averaging latent embeddings inferred by encoders of respective modalities. However, the need for explicit pairing limits their applicability in cases where cross-modality correspondences are incomplete or noisy. JAMIE IT incorporates the manifold alignment approach into the VAE framework, and UniPort (6] takes advantage of partially paired features and coupled VAE, but they still confront computational intensity in dealing with large-scale clinical or experimental datasets.
Another prominent line of work aligns modalities through unsupervised manifold matching, optimiz- ing for geometric consisteney between latent spaces. UnionCom (5] aligns modalities by constructing a KNN graph and applying unsupervised linear manifold aligmment, while CMOT (39] adopts non- linear manifold alignment with partial supervision. SCOT [4 leverages Gromov-Wase Wasserstein optimal transport (GWOT) similarity matrices and uses barycentric projection for integration, with following revised versions such as Pamona 77 and SCOTv2 [3] by imposing regularizations on GWOT, while SCOOTR [15] aligns both samples and features using co-optimal transport (COOT). These methods typically require constructing pairwise similarities and a global coupling matrix, restricting scalability to large datasets due to computational bottlenecks, and in practice, they are often validated only on limited sample sizes or toy examples. Moreover, they often focus on the integration of two modalities, leaving the integration of more omics layers underexplored challenge.
Recent works, such as scTFBridge [34), scMaui (20). and InClust+ [35), have discussed integration based on latent decomposition. However, they still rely on designs like partial pairing supervision, stacked encoders, and cross-moda contrastive learning, limiting their scalability completely unpaired and multi-omics contexts. In contrast, we aim to achieve the decoupling via unified 3- VAE composed of a single sample, thereby ensuring flexibility and scalability in completely unpaired data across multiple omics. Theoratically, such disentangled subspaces are unidentifiable (i.e., not unique) without additional constraints (21). We leverage this unidentifiabiliiy 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 entire space while aligning different modalities.
treating observations in different omics equally as a single
Methods
3.1 Preliminary: Disentangled VAE
Variational Autoencoders (VAEs) 22 are a class of generative models that learn probabilistic mapping between observed data r and latent variable space z via variational inference by introducing an encoder network to parametrize the variational posterior qa(z x) and a decoder network to reconstruct the generative process pa z). The model is trained by maximizing the evidence lower bound (ELBO) on the marginal logllikelihood:
ELBO (I:) (sle |²)] KL (x) p(=),,
where (L(g || p) denotes the Kullback-Leibe (KL. divergence between distributions & and p. The first term encourages faithful data reconstruction, while the second regularizes the latent space to align with the prior.
3

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Gene leve. Modality
Feature
index
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Gete acticry score
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Decnder p(rja))
Chromatin accessibility
Masio features
Prosein ooding
Modallty-shured component 7
Musked recostraction loxe for unmeasured fextures
Od1
Surface protein
Isometric regulacization
Adversarial regularization
Distance stracture
Modality-shred compoonent
Medalat- shared compenent
Tool
Preserve
Generator (B-VAF)
Discriminaton
latent
space
Figure 2: Overview of the proposed scMRDR. We employ 3-VAE to disentangle omics-specific and omics-shared latent representations, and impose isometric loss and adversarial training as regularization to encourage modality integration and bio-conservation.
Classical VAE often conflates modallty-sharees and coddality-speciffe signals in the latent space, impeding interpretability and downstream analyses. To improve disentanglement in the learned latent representations, VAE [99] introduces hyperparameter / > 1 to upweight the KL divergence term in the VAE objective
ELBO))VAE(T) = (= (= x)] - B (L x) p(z)).
(2)
higher value of B3 enforces stronger constraint the latent space, promoting disentangled and interpretable representations at the cost of reduced reconstruction accuracy.
Simply disentangling the latent space does not guarantee that the shared latent components from different omics data are fully aligned in distribution, nor does ensure that the shared latent components preserve the structural information present in the original data. Such structural information is captured by the VAE in the entire latent space and may not necessarily be retained within the shared subspace. We will impose additional regularization on the disentangled latent space generative model designed for single-cell multi-omics to address the issue.
Medaliyvindos
buerty
Interifueter
shared lotent festor
Mean proportion
TE
Diopout rite
3.2 Disentangled generative model for multi-omics data
Usiay aus
Dipersion
(m)
To achieve flexible and scalable integration, we propose a gen- erative model tailored for single-cell multi-omics data (Fig()). generated
Cheerues coutte
We assume that observations (m) in the omics from latent embeddings lying in two independent subspaces, i.c. common latent variables shared across modalities and
Figure 3: Graphical illumination of the single-cell multi-omics data generative model.
modality-specific latent variables (m) and we have
and p(2 p(z.)(( (22))(((2lm))
(3)
= blb.aaaaeeccccmemmmmmmme pccp:pppccpaalplppppppppppp.. c)(z,,
where represents other covariates, such the experimental batch during sequencing. Batch effects are systematic variations introduced by non-biological factors, including differences experimental runs, reagent lots, operators. These effects obscure true biological signals or introduce spurious

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patterns in the data 32]. included covariate in the modeling process.
To mitigate such confounding influences, batch information is commonly
Sequencing reads of scRNA, protein, and other omics data can all be mapped to the gene level (e.g., gene activity scores derived from peak aggregation in single-cell ATAC-seq)- Since the read matrix are typically sparse (with both biological and technical dropouts) count data with over-dispersion (i.e., the variance exceeds the mean), we parametrize the generative process p(z z, c) using a zero-inflated negative binomial (ZINB) distribution (24, 29] (which can be changed to ordinary Gaussian model normalized scores or more non non-count data included), i.e.,
Zng To + (1 Kng NB((1.Png: Tn) A ZINB ZINB(laPng) Tg. Wg)
(5)
where óg is point mass at zero, in represents the library size of cell n. png is the mean proportion of the corresponding measurement (RNA expressions. activity score, protein level, etc.) of gene g in cell n, rg is the dispersion factor of gene g. Tag is the dropout rate of gene g in cell n. We parametrize the parameters by some non-linear neural networks follows h fx(2,c), Png [h),,, Wng fx()).
Prior distributions of latent factors are assumed isotropic multivariate Gaussian distributions,
ie., p(=s (m) - (Jum: o 1) and p(=u _ (O 7). We employ variational posteriors {(=u|2)) (x) + on (x) o (0, 1) and (22, z., m) = (z, m) + oz(2, () @N(0, I) to approximate the prior, and the loss function (negative ELBO) of 3-VAB is
L.S.VR- - ELBO Lresnn + BLII.
(6)
---gg(=l... log p(z|z, c) +
+ (L)](z/
where 3 > 1 to encourage the disentanglement of zu and For the ZINB model, the reconstruction loss, i.c. the expected log likelihood under the variational posterior,
E B log p()]2,c)) En Eg log PANBBEE InPng Tg. kng))
where PZINB(X (X 2;, xll==o + (1 π) PNB and PNB (x; r) stands for the probability mass of negative binomial distribution ((,.r)) at x, i.e. PNB (,,)) T(xtr) [r)
particular, the probability mass zero PNB (O (0:p,)) = r+
3.3 Adversarial regularization for omics integration
By disentangling the latent space, we obtain, in general, modality latent variable zn lying in shared subspace. To further encourage the alignment of distributions 2 from different omics, we impose an additional adversarial regularization [17 16 by introducing m--class discriminator D(=w): Rdd -> (0, 1,...,m) to distinguish 2, of samples from different omics and try to optimize its capacity, i.e.
min Ldiscriminator min
Σ log(
log D(=(m)))
(m) Zu
(8)
while training the VAE encoders to fool the discriminator as much possible by optimizing in the opposite direction
max inf Ediscriminator (l 2)
(9)
which is cquivalent to
Σ m log (D(a!m)) m
min Calignment min sup ((ali))
(10)
((Fu
achieving proper alignment of embeddings from different omics ultimately.
3.4 Isometric loss for structure preservation
To ensure that 2, captures the biological differences between samples (e.g., cell types), we introduce an additional unsupervised snncture-preservving regularization, since cell type labels are typically
5

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unavailable. Though the original feature matrices are high dith-mimensionl,, the full latent representation (Zu: 2g) learned by the generative model effectively preserves mntr--moaaliyy structure. Hence, we reformulate the problem as encouraging to retain the structural information of the full latent space. Specifically, since the latent embeddings already reside in a low-dimensional space, we apply an isometric loss [I that minimizes the discrepancy between the pairwise Euclidean distance matrices computed from and from Zus for each modality, i.c..
Lyreeseree
Σ
Σ TR (JEX(m)
[[0=_,(0a) M4., (1ry) (1,=(m;) - 14= (1
(11)
where Ms,, (3:) is the posterior mean of variational approximation ((2u(ar) and uz is the posterior mean of total latent embeddings (g(2 z, (2), (2,,11, m)).
And the total optimization goal for VAE becomes
Liaal = Lreamm + 3LKl. aalignmmnt + ? Creserrve
(12)
In the training process, we first update the discriminator by optimizing Edisoriminator then update VAE with respect to the total loss Liaal in turn in each mini-batch.
3.5 Masked reconstruction loss for missing features
In unpaired multi-omics datasets, different modalities are measured separately and often originate from distinct sources. Although it is possible to align features across modalities at the gene level, severe missing features still exist due to different sequencing coverages, especially for antibody- -asse protein profiling techniques such as CITE-seq, which typically covers only few hundred proteins due to the limited availability of antibody markers [4), while tens of thousands of genes can be measured in other omics. Restricting the analysis to the overlapping features across all modalities would lead to substantial information loss, whereas naively imputing unmeasured features with zeros would severely distort the data distribution. To address this, introduce binary mask b {0, 1) indicating feature availability that prevents gradients from backkpropagating through unmeasured features in the reconstruction loss for each modality, and then scale by the proportion of available features to ensure that the reconstruction loss for each sample is on a comparable scale, i.e.,
N
Lreenn
1
G
Σ bug log [PZINB(Iri PaPng rg. Rng)]
(13)
N
Eg=1 bug g=1
The masked loss strategy ensures that the model can fully utilize the available information while preserving the integrity of the original data distribution.
Results
4.1
Setup and evaluation metrics
To verify the effectiveness of our proposed method, we comprehensively evaluate scMRDR through a series of experiments, beginning with standard benchmarks and then scaling up to more complex single-cell and multi-omics scenarios. We employ publicly available datasets from previous researches Detailed setups are shown in Appendix [. Jnnd Table 2] We compare to state-of-the the-th--tt art baselines, including GLUE, VI, Seurat v5, Harmony, JAMIE, and so on, and evaluate in terms of cell-type clustering. modality integration, and batch removal. Cell-type labels in different omics has been aligned in evaluation. It should be emphasized that we did not use cell-type labels during training. UMAP visualizations are presented for qualitative comparison. For quantitative evaluation, the following commonly used metrics (Appendix (A.2) (A.2) are
with curated cell-type annotations [28 37 25
included: Fl isolated label scores, k-means NMI, k-means ARI, cell-type Silhouette, and cell-type separation LISI (cLISI) to evaluate the performance in cell type conservation, modality Silhouette,
modality integration LISI (iLISI,, kBET, Principal Component Regression (PCR) R²² and graph connectivity to evaluate the performance in modality integration, as well as batch Silhouette, batch integration LISI (iLISI), kBET, and PCR R² to evaluate the performance in batch effect correction 26 36).
We evaluate and visualize all the above metrics based on the package scib-metrics 266 The overall score is calculated as a weighted average of all metrics on bio-conservation (40% weights), modality integration (30% weights), and batch correction (30% weights).

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TE SEWTTTA
THE AUC
FOR
QUA
2-42
4:42
0.47
JAPEE
500
Figure 4: Performance comparisons on two-omics integration, where unscaled metrics calculated via scIB are reported.
TCWEER
TMCT
Figure 5: Performance comparisons on two-smics integration with scale dataset, where unscaled metrics calculated via seIB are reported. The default preprocessing method seglue.data.ls for GLUE fails to handle the large-scale data, and substituting it with PCA leads to severe performance degradation, although using "TruncatedSVDD VD' approximation of LSI can alleviate this issue.
4.2 Benchmarking performance on two-omies integration
We first compare ScMRDR with 9 existing methods, including Seurat v5 18 Harmony 23 VC
24], ScGLUE [8), JAMIE [II, UnionCom [5). Pamona (7), MaxFuse 10 and SIMBA ( on
a unpaired scRNA and SCATAC dataset of human kidney tissue 28 Among these, Vc can be regarded baseline counterpart of our model, with no disentanglement regularization applied to the latent space. The dataset contains scRNA-seq with 27. 146 genes on 19,985 cells and scATAC-seq with 99,019 peaks on 24,205 cells. Peak signals in ScATAC are aggregated to gene-level activity score in scMRDR by the package episcanpy (12]. Gene activity scores are also used in integration by Seurat, Harmony, and VI, while others use raw peak signals directly. We choose the highly variable genes for each omics and take the union as input. Shown in Fig scMRDD outperforms the existing methods, exhibiting an excellent performance in modality integration, bio-conservation. and batch correction. As shown in Fig 6a] without the incorporation of explicit cell type annotations in training, our method yields well-separated embedding clusters corresponding to distinct cell types in an unsupervised way, thereby preserving the underlying biological heterogeneity. Meanwhile, samples from different omics and batches fuse and align well in the latent space, demonstrating successful correction of modality-specific variations and technical noises like batch effects. In contrast, some other methods such as Harmony, se VI and JAMIE (Fig in Appendix (A.5) can preserve biological differences between distinct cell types, but fail to integrate the distributions of the two different omics modalities.
4.3 Scalability on integration with large-scale dataset
To validate the scalability of scMRDR on larger datasets, we evaluate the performance on an large- level dataset on mouse primary motor cortex with more cells available [37]. This large-scale data includes 69,727 cells with measurements on 27,123 genes by ScRNA-seq and 54,844 cells with measurements on 148,814 chromatin peaks by ScATTCC-sq. Methods based on optimal transport or other unsupervised manifold alignment, such as JAMIE, UnionCom, and Pamona, fail to run on datasets with such scale due to errors in memory or optimization. We compare the performance of the rest methods. Shown in Fig some methods that perform well on small-scale datasets suffer significant performance drops larger ones (Fig 10 in Appendix A.5) For example, GLUE exhibits
7

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(b) UMAP visualization large-scale two-omics dataset
Figure 6: UMAP visualization of the latent representations obtained by scMRDR in the two-omics integration task. Latent embeddings of other methods are shown in Appendix A.5 An effective method should yield well-separated clusters corresponding to distinct cell types, and fuse samples from different modalities and experimental batches in sequencing. Noted that the annotated cell type labels are not incorporated in the unsupervised learning but only used in evaluation.
1Mars
CF DETOREOS CONDE CREENEE FRghAs
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120
125
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Figure 7: Performance comparisons on triple-omics integration, where unscaled metrics calculated via scIB are reported.
strong susceptibility to the choice of preprocessing strategy which itself markedly dependent on data scale, whereas method maintains stable performance large-scale datasets (Fig/6b). This makes it highly scalable for large-level single-cell data integration, enabling the informative linking among different omics and providing more valuable biological insights.
4.4 Scalability on triple-omics integration
Most existing methods do not support integrating datasets with more than two omics, while scMRDR naturally extend to the integration of triple-omics
more. To illuminate it, we conduct case study on integrating ScRNA, ScATAC, and CITE-seq measured sc-protein levels, using a dataset on human bone marrow 225. We conducted integration on 30,486 cells with scRNA-seg on 13,431 genes, 10,330 cells with ScATTC-seq on 16,490 peaks, and 18,052 cells with 134 surface proteins measured by CITE-seq. Some methods that perform relatively well on two-omics datasets, such as Seurat v5, are not suitable for integrating more modalities, as they require dictionary learning and bridge integration between two omies. As result, we compare the performance of the existing methods that support triple-omict integration, including GLUE, ScVI, and Harmony. Shown in Fig 7 scMRDR shows consistently excellent performance in the integration task with more modalities the contrary, methods like GLUE fail to align latent distributions over three omics, especially when one of the omics modalities (proteomics here) significantly fewer measured features than the others (Fig 8

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Figure 8: UMAP visualization of the unified embeddings in triple-omics data.
4.5 Ablation study and sensitivity analysis on the regularized beta-VAs VAE
To demonstrate the effects isometric and adversarial regularization within the 3-VAE framework. we conducted ablation experiments and sensitivity analysis with a range of different hyperparameter combinations on the two-omics human kidney datasets. Shown in Table with different hyperparam- eters, scMRDR performs consistently better than the ablation results when removing any individual component, and the worst model is the baseline without any regularization. The absence isometric constraints modality-advent adversarial regularization leads substantial drop in performance, where isometry more essential to bio-conservation while adversary more vital to modality alignment. The influence of /3 is relatively minor as the structured prior imposed on inherently promotes disentan- glement. Nevertheless, employing moderately large 3 can increase the conditional independence between ou and 2., thereby enhancing the efffcctiveness of latent disentanglement. While different hyperparameter combinations have certain impact due to trade-off's among various losses and the influence of randomness, the performance are generally robust to the choices.
We also conduct ablation studies on a triple-omics dataset evaluate the effectiveness of the masked loss. The results (Table in Appendix A.4) show that, keeping all other hyperparameters unchanged, simply setting the missing features in the proteomics to zero without applying a loss mask leads to significant performance drop. This highlights the importance of our masked loss strategy in effectively handling integration tasks where some omics layers (e.g., scProtein) contain substantially fewer features compared to other modalities.

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Table 1: Performance in ablation studies and sensitivity analysis, where unscaled seIB aggregate scores are reported
7
Total Score
Batch-correct
Bio-conserve
Modal-integrate
Notes
2
$
0.66
0.52
0.74
0.70
2
7
0,65
0.54
0.69
0.72
2
5
0.65
0.55
0.69
0.71
2
2
0.65
0.50
0.72
0.70
2
5
0.65
0,49
0.70
0.73
0.65
0.47
0.71
0.74
0.64
0.49
0.68
0.75
3
0.64
0,48
0.71
0.71
4
5
0.64
0.47
0.71
0.72
2
10
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0.68
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2
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2
0
0.61
0.51
0.60
0.72
0
0.59
0.48
0.63
0.66
Baseline
4.6 Biological significance of integrating single-cell and spatial omics
To better evaluate the biological significance of scMRDR, we integrated scRNA 37 ScATAC 37] and spatial transcriptomies (merFISH) (38] of mouse primary motor cortex 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 (Fig. 12 in Appendix).
Due to the low coverage of merFISH (only 254 genes measured), only 103 genes detected as spatial variable genes (SVGs) by SPARKX (Padj < 10-29). We leveraged the spatially interpolated scRNA data (26069 genes) and 4095 SVGs (Padj < 10-20) are detected. We replicated 83 out of 101 SVGs detectable by merFISH (like Lamb5, Calbl, Cux2), and also revealed new SVGs (like Hs3st4, 0pa6, Zfhx4). Similarly, using ScATAC with imputed spatial locations, we identified 142 SVGs in gene activity scores (Padj < 10-29), including several key transcription factors like Zfhx4, Cuxl, Cux2, Gpc5. This will further support the investigation of spatially specific regulatory mechanisms.
Discussion
Conclusion. In this paper, we propose a principled and feasible generative model named scMRDR to integrate unpaired multi-omics single-cell data into unified latent space. We employ V-V to disentangle latent embedding into modal-shared and modal-specific subspace, incorporating isometric regularization to ensure the conservation of biological information within each omics, and adversarial loss encourage the fusion of different modalities. Masked loss are adopted address the feature- missing issue in different modalities. Via empirical experiments and comprehensive comparison with existing methods, scMRDR exhibits an excellent performance modality integration, bio- conservation, and batch correction, and demonstrates strong adaptability for scaling to larger, large- level datasets with more omics modalities to integrate.
Limitations. There are still some limitations to our approach. The regularized 3-VAE introduces the trade-off between different optimization goals, reflecting the choices of hyperparameters 3, and 7. In particular, the introduction of the adversarial loss, i.e., the min-max optimization objective, increases the training difficulty. Besides, we map features of all modalities to the gene level, such as aggregating ScATAC-seq peak signals into gene activity scores. Although selective masking in the loss allows for partially unmatched features, it may still introduce potential information loss.
Outlooks. In addition to measuring various omics features within cells, emerging spatial multi-omics technologies allow us capture the spatial coordinates of cells, further enriching cellular information. Meanwhile, perturbation sequencing enables the observation of cellular responses actoss omics layers various chemical treatments and genetic perturbations (c.g., CRISPR). Integrating spatial and dynamic information across modalities under different conditions will be an important direction for future exploration and extension of scMRDR.
10

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13

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A Technical Appendices and Supplementary Material
A.1 Details on experiments
The species, tissues, sample sizes, modalities, and references (the original sources) of the single-cell datasets used in the experiments are shown in Table [ In our experiments, we set the batch size to 128, the epoch number to 200, and the dimensions of both the shared latent component (d,,) and mppelit component (d,) to 20. Parameters are optimized via Adam optimizer and the learning rate is started from 0.001 with cosine annealing scheduler. Other hyperparameter settings are summarized in Table 2 10% of the data was used as a validation set for early stopping during training based on the total loss validation set. For scATAC-seq data, peak count signals are converted to gene-level gene activity scores using EpiScanpy. For datasets integrating two modalities, select highly variable genes that measured in both scRNA-seq and SCATCCse (based on gene activity scores) as input features, and do not apply masked loss. For tri-modal integration, use highly variable genes from scRNA-seq and ScATAC-seq. well as all genes with nonzero measurements in seProtein as input features, and apply masked loss according to the available gene list associated with each modality.
Competing methods are used with their respective default settings. Specifically, Seurat, Harmony, and VI use gene activity scores for scATAC-seq. while all other methods operate on the original peak counts.
We run all empirical experiments on a single NVIDIA RTX 4080 GPU. The runtime of our method for 200 epochs also reported in Table 2
A.2 Evaluation metrics
F1 isolated label scores. The optimal F1 score by optimizing the cluster assignment of the isolated label using the Fl score across Louvain clustering (resolutions 0.1-2, step 0.1). The metric is averaged across all isolated cell-type labels.
Silhouette scores. The global silhouette width measures (ASW) between isolated and non-isolated labels on the PCA embedding. scaled to [O, 1]. ASW measures how similar a data point is to its own cluster compared to other clusters, with higher ASW indicating more compact and well-separated clusters. For the bio-conservation, ASW was computed and averaged across cell identity labels; while for modality batch integration, ASW was computed and averaged across batch modality labels, and then subtracted from to ensure higher scores indicate better integration.
Kmeans NMI. Normalized Mutual Information (NMI) measures the similarity between clustering results and known labels, accounting for label permutations. We compute NMI between KMeans clusters and ground truth labels, with scores ranging from 0 (no overlap) to (perfect match).
Kmeans A RLL Adjusted Rand Index (ARI) evaluates clustering accuracy by considering both agree- ments and disagreements between predicted and true labels, adjusted for chance. We compare KMeans clusters with ground truth labels, where indicates random labeling and indicates perfect agreement.
Graph LISI. Graph LISI is extension of the original LISI metric that is computed from neigh- borhood lists per node from integrated kNN graphs. Instead of relying on a fixed number of nearest neighbors, Graph LISI computes shortest-pan distances the integrated graph to consistently define neighborhoods for each cell, providing a stable diversity score even when the underlying graph has variable connectivity. The resulting scores are rescaled to 0-1 range, where higher values indicate better batch or modality integration (iLISI) or better cell-type separation (cLISI).
Principal component regression. Principal Component Regression (PCR) is used to quantify batch effects by assessing how much variance in the data can be attributed to batch variables or modality differences, which is computed by multiplying the variance explained by each principal component (PC) with the R² value from regressing the batch on that PC and then summing over all PCs.
kBET. k-nearest neighbor Batch Effect Test (kBET) assesses data mixing by checking whether the local batch label distribution in each cell's neighborhood matches the global distribution. reports a rejection rate across tested neighborhoods, where lower rate indicates better batch mixing.
14

---

Running
20min
120min
50min
time
Masked loss
Hyperparameters
No
No
Yes
X
5
5
10
7
5
10
Table 2: Details on the single-cell datasets and experimental settings.
3
2
2
5
Reference
28
37
255
Sample size
19,985
24,205
69,727
54,844
30, 18,486
10,330
18,052
scProtein (CITE-seg)
ScRNA-soe seg SCATAC ScATAC-seq seq
ScATAC-seg
ScATAC-seq
scRNA-sen
scRNA-seg
Modality
motor cortex
Bone marrow
Kidney
Primary
Tissue
Species
Human
Mouse
Human
small size two-omics
large seale two- -omis
triple-omics integration
integration
integration
Dataset
15

---

Graph connectivity. Graph connectivity, ranging from 0 to I, measures how well cells of the same identity are connected within the integrated kNN graph. For each cell type, computes the fraction of cells in the largest connected component of that type's s subgraph.
A.3 Metric values in experiments
Unscaled metric values in all experiments shown in Table We directly used unscaled values calculate aggregate scores.
A.4 Ablation study and sensitivity analysis
We conducted ablation experiments and sensitivity analysis the two-omies human kidney datasets to demonstrate the effects of applying isometric loss and adversarial learning regularization within the 3-VAE framework. The results have been shown and discussed in the main text (Table D
To evaluate the effectiveness the Masked loss, we also conduct ablation studies on a triple-omics dataset. The results (Table indicate that simply setting the missing features in the proteomics to zero without applying loss mask leads to significant performance drop. This highlights the importance of our masked loss strategy in effectively handling integration tasks where some omics layers (e.g.. scProtein) contain substantially fewer features compared to other modalities.
A.5
UMAP visualization experimental results
We employ UMAP to visualize the results of multi-omics integration, where each point denotes the low-dimensional representation an individual sample. effective integration method should yield well-separated clusters corresponding to distinct cell types, thereby preserving the underlying biological heterogeneity. Concurrently, samples originating from different omics modalities and batches should be well-aligned in the embedding space, reflecting successful correction of modality- specific and batch-specific technical variations.
A.6 Spatial location imputation via integration of single-cell and spatial omics
We integrated scRNA, ScATAC, and spatial transcriptomics (merFISH) data in mouse primary motor cortex using scMRDR, and then interpolated the missing spatial locations single-cell data by conducting optimal transport between the aligned latent representation of samples with spatial locations (merFISH) and samples without spatial information (scRNA and scATAC). We visualized the imputed spatial locations labeled by the cortex layer annotations provided by the original datasets (Fig. 12)
16

---

PCR
0.99
0.99
0.85
1.00
0.99
1.00
0.99
0.83
0.64
1.00
1.00
1.00
1.00
0.95
0.68
0.96
1.00
0.85
1.00
0.99
0.70
0.00
GC
0.96
0,94
0.71
0.91
0.46
0.43
0.45
0.03
0.59
0.41
0.95
0.80
0.75
0.82
0.58
0.48
0.45
0.07
0.87
0.82
0.46
0.40
modality infegration
kBERT
0.32
0.34
0.00
0.19
0.34
0.09
0.08
0.00
0.06
0.00
0.10
0.07
0.11
0.00
0.00
0.00
0.01
0.10
0.06
0.09
0.00
0.00
iLISI
0.37
0.60
0.00
0.15
0.00
0.00
0.00
0.00
0.00
0.00
0.26
0.01
0.10
0.00
0.00
0.00
0.00
0.00
0.28
0.15
0.00
0.00
ASW
0.86
0.85
0.81
0.87
0.70
0.74
0.56
0.90
0.56
0.38
0.82
0.77
0.52
0.72
0.57
0.41
0.66
0.89
0.83
0.85
0.76
0.51
PCR
0.26
0.09
0.37
0.00
0.00
0.61
0.81
0.95
0.00
0.00
0.97
0.98
0.98
0.93
0.67
0.95
0.99
0.85
0.31
0.25
0.53
0.12
batch correction
kBERT
0.38
0.28
0.29
0.19
0.19
0.26
0.27
0.27
0.27
0.39
0.14
0.09
0.09
0.11
0.09
0.05
0.10
0.16
0.13
0.32
0.11
Table 3: Unscaled metric values in experiments
iLISI
0.52
0.42
0.47
0.16
0.06
0.51
0.26
0.70
0.19
0.43
0.24
0.18
0.23
0.12
0.10
0.14
0.13
0.12
0.27
0.20
0.20
0.17
ASW
0.90
0.90
0.95
0.89
0.90
0.93
0.86
0.98
0.89
0.81
0.90
0.86
0.90
0.94
0.93
0.70
0.66
0.98
0.83
0.86
0.90
0.76
cLISI
1.00
1.00
1.00
1.00
1.00
0.96
1.00
0.76
1.00
0.98
1.00
1.00
0.99
1.00
1.00
0.99
0.97
0.73
1.00
1.00
1.00
1.00
ASW
0.66
0.67
0.56
0.59
0.68
0.50
0.43
0.49
0.54
0.44
0.56
0.61
0.53
0.52
0.51
0.42
0.40
0.49
0.61
0.59
0.54
0.44
Moo-conservation
ARI
0.58
0.57
0.43
0.49
0.61
0.18
0.17
0.01
0.41
0.08
0.37
0.51
0.33
0.26
0.21
0.21
0.01
0.00
0.38
0.55
0.31
0.16
NMI
0.76
0.77
0.68
0.73
0.78
0.22
0.30
0.01
0.60
0.43
0.58
0.69
0.55
0.57
0.47
0.38
0.26
0.01
0.68
0.67
0.50
0.35
0.69
0.65
0.59
0.65
0.68
0.50
043
0.49
0.54
0.42
0.58
0.61
0.53
0.53
0.52
0.44
0.42
0.49
0.57
0.55
0.53
0.45
IL
Modal integrate
0.70
0.74
0.47
0.62
0.50
0.45
0.42
0.35
0.37
0.36
0.62
0.53
0.49
0.50
0.37
0.37
0.42
0.38
0.61
0.58
0.38
0.18
oggregate Score Bio
conserve
0.74
0.73
0.65
0.69
0.75
0.47
0.47
0.35
0.62
0.47
0.62
0.68
0.59
0.57
0.54
0.49
0.41
0.35
0.69
0.67
0.58
0.48
Batch correct
0.52
0.42
0.52
0.31
0.29
0.58
0.35
0.73
0.34
0.41
0.56
0.53
0.55
0.52
0.45
0.47
0.46
0.51
0.39
0.36
0.49
0.29
Overall ore
tmple wel--mmmiinttgratiiee attton
omlesintegration
0.66
0.64
0.56
0.56
0.54
0.50
0.48
0.46
0.46
0.42
0.60
0.59
0.55
0.54
0.46
0.45
0.43
0.41
0.58
0.55
0.49
0.33
large- wes-ssalllwwoo
GLUE(PCA)
GLUE(LS))
Com
GLUE
MaxFuse
Seurat
Pamona
JAMIE
SIMBA
Harmony
Seurat
Harmony
MaxFuse
SIMBA
GLUE
Harmony
Ours
scV1
Ours
seVI
Ours
ScVI
17

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DOS ONE
4.0
1000500.00
P
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LAAPE
UMAVE
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LIAPT
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Seurst
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SUSVONE 36
2000
JAME
400
2400
LMAFE
(MA7)
MBBA
1000
52000N0 TV
PP VOAN
Rec
Figure 9: UMAP visualization of the unified embeddings in small-scale two-omics data integration.
18

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balth
EOOREHS E4
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Figure 10: UMAP visualization of the unified embeddings in large-scale two-omics data integration.
19

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Table 4: Ablation study in triple-omics data, where unscaled selB aggregate scores are reported.
Overall score
Batch correct
Bio conserve
Modal integrate
Ours
0.58
0.39
0.69
0.61
beta=1
0.51
0.39
0.58
0.52
lambda=0
0.48
0.32
0.60
0.49
gamma=0
0.53
0.40
0.58
0.58
w/o masked loss
0.44
0.33
0.58
0.37
(+)
cell Eypee
modallty
beich
UNMAY2
sooren0 6B
UMAP1
UMMPP1
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banch
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LINA11
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51.5
51.2
5263
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AcceweO
2245
23d2
CD4
5201
Erythrodd
DC
ATAC ReStein
Progeritrr
Figure 11: UMAP visualization the unified embeddings in triple-omics data.
20

---

BICCN subclass_eas _abell
Astrocytes Endothelial
Microglia
LS_IT
Oligodendrocytes
PT
Kppatialz
16_TT
Pericytes
Pvalb
L6_ L6_IT_Card Car3
L6b
Sncg
L23_IT IT
Sst
L45. IT
Chodl
L56_NP
Lamp5
Vip
X spatiall
(a) Spatial plot of the merFISH data with originally measured spatial locations.
cell_ sell_type
cell_type
L2/3 IT
L4I5
L4/5 IT
L5 ET
LG CT
L6
5pallar2
Lamps
Lamp5
NP
Pvalb
Pvalb
Sncg
Sncg
Sst
Vip
spatial1
spatial1
(b) Spatial plot of the scRNA data with imputed spatial locations.
Spatial plot of the ScATAC data with imputed spa- tial locations.
Figure 12: Spatial plots of merFiSH and spatially imputed scRNA and scATAC data.
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Reviews:
[{"review_id": "GG1YqIwC7Q", "reviewer": "Reviewer_XHw7", "summary": "This paper proposes an algorithm to enable multi-omics integrations on unpaired data. The authors design a disentangled VAE using the framework of $\\beta$-VAE and add new regularization terms to enable the model achieves common latent space. The authors examined their model using several multi-omics datasets.", "questions": "1. The latent embeddings are split into two parts, shared and exclusive. Which one is used to produce UMAP and further analysis?\n2. In Figure 4, for the PCR comparison of batch correction, the result of the proposed method is 0. Is it a typo? If not, what issue causes this abnormal result?\n3. I would like to see whether the disentangled features are able to capture the meaningful representation.\n4. In Figure 6, does the cell type label align between RNA-seq and ATAC-seq?", "limitations": "See my questions", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. Clear writing. I really enjoy the clear writing which has a very readable manuscript.\n2. The integration of unpaired multi-omics data is an important topic.\n3. The proposed method is clear and achieves a good performance compared to baselines.\n\nWeaknesses:\n1. Some results in the experiment section needs further clarifications.\n2. The compared baselines are a little bit outdated. The latest baseline is GLUE, which was published three years ago.", "was_revised": true, "final_justification": "I appreciate authors' effort on providing detailed benchmarks in a short time, and I think this rebuttal has addressed all my concerns. I will raise my points accordingly. Please make sure to include these additional benchmark in the future version.", "rebuttal": "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.\n1. Explantions on experimental results \n\n* 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)\n* we attached the original unscaled metrics in the appendix (Table 2). We also mentioned that in the captions of Figures 4, 5, and 7.\n* 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)\n2. Comparison with recently published methods\n\nWe 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, \n* 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; \n* 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.\n### performance on two-omics integration\n||aggregate score||||bio-conservation|||||batch correction||||modality integration|||||\n|----------|:---------------:|:-------------:|:------------:|:---------------:|:----------------:|:-----:|:-----:|:-----:|:-----:|:----------------:|:-----:|:-----:|:-----:|:--------------------:|:-----:|:-----:|:-----:|:-----:|\n||overall|batch correct|bio conserve|modal integrate|IL|NMI|ARI|ASW|cLISI|ASW|iLISI|kBERT|PCR|ASW|iLISI|kBERT|GC|PCR|\n|Ours|0.66|0.52|0.74|0.70|0.69|0.76|0.58|0.66|1.00|0.90|0.52|0.38|0.26|0.86|0.37|0.32|0.96|0.99|\n|GLUE|0.64|0.42|0.73|0.74|0.65|0.77|0.57|0.67|1.00|0.90|0.42|0.28|0.09|0.85|0.60|0.34|0.94|0.99|\n|scVI|0.56|0.52|0.65|0.47|0.59|0.68|0.43|0.56|1.00|0.95|0.47|0.29|0.37|0.81|0.00|0.00|0.71|0.85|\n|MaxFuse|0.56|0.31|0.69|0.62|0.65|0.73|0.49|0.59|1.00|0.89|0.16|0.19|0.00|0.87|0.15|0.19|0.91|1.00|\n|Seurat|0.54|0.29|0.75|0.50|0.68|0.78|0.61|0.68|1.00|0.90|0.06|0.19|0.00|0.70|0.00|0.34|0.46|0.99|\n|Pamona|0.50|0.58|0.47|0.45|0.50|0.22|0.18|0.50|0.96|0.93|0.51|0.26|0.61|0.74|0.00|0.09|0.43|1.00|\n|JAMIE|0.48|0.55|0.47|0.42|0.43|0.30|0.17|0.43|1.00|0.86|0.26|0.27|0.81|0.56|0.00|0.08|0.45|0.99|\n|SIMBA|0.46|0.73|0.35|0.35|0.49|0.01|0.01|0.49|0.76|0.98|0.70|0.27|0.95|0.90|0.00|0.00|0.03|0.83|\n|Harmony|0.46|0.34|0.62|0.37|0.54|0.60|0.41|0.54|1.00|0.89|0.19|0.27|0.00|0.56|0.00|0.06|0.59|0.64|\n|UnionCom|0.42|0.41|0.47|0.36|0.42|0.43|0.08|0.44|0.98|0.81|0.43|0.39|0.00|0.38|0.00|0.00|0.41|1.00|\n### Performance on large-scale two-omics integration\n||aggregate score||||bio-conservation|||||batch correction||||modality integration|||||\n|-----------|:---------------:|:-------------:|:------------:|:---------------:|:----------------:|:-----:|:-----:|:-----:|:-----:|:----------------:|:-----:|:-----:|:-----:|:--------------------:|:-----:|:-----:|:-----:|:-----:|\n||overall|batch correct|bio conserve|modal integrate|IL|NMI|ARI|ASW|cLISI|ASW|iLISI|kBERT|PCR|ASW|iLISI|kBERT|GC|PCR|\n|Ours|0.60|0.56|0.62|0.62|0.58|0.58|0.37|0.56|1.00|0.90|0.24|0.14|0.97|0.82|0.26|0.10|0.95|1.00|\n|Seurat|0.59|0.53|0.68|0.53|0.61|0.69|0.51|0.61|1.00|0.86|0.18|0.09|0.98|0.77|0.01|0.07|0.80|1.00|\n|GLUE(LSI)|0.55|0.55|0.59|0.49|0.53|0.55|0.33|0.53|0.99|0.90|0.23|0.09|0.98|0.52|0.10|0.11|0.75|1.00|\n|scVI|0.54|0.52|0.57|0.50|0.53|0.57|0.26|0.52|1.00|0.94|0.12|0.10|0.93|0.72|0.00|0.00|0.82|0.95|\n|Harmony|0.46|0.45|0.54|0.37|0.52|0.47|0.21|0.51|1.00|0.93|0.10|0.11|0.67|0.57|0.00|0.00|0.58|0.68|\n|GLUE(PCA)|0.45|0.47|0.49|0.37|0.44|0.38|0.21|0.42|0.99|0.70|0.14|0.09|0.95|0.41|0.00|0.00|0.48|0.96|\n|MaxFuse|0.43|0.46|0.41|0.42|0.42|0.26|0.01|0.40|0.97|0.66|0.13|0.05|0.99|0.66|0.00|0.01|0.45|1.00|\n|SIMBA|0.41|0.51|0.35|0.38|0.49|0.01|0.00|0.49|0.73|0.98|0.12|0.10|0.85|0.89|0.00|0.10|0.07|0.85|\n### Performance on triple-omics integration\n||aggregate score||||bio-conservation|||||batch correction||||modality integration|||||\n|---------|:---------------:|:-------------:|:------------:|:---------------:|:----------------:|:-----:|:-----:|:-----:|:-----:|:----------------:|:-----:|:-----:|:-----:|:--------------------:|:-----:|:-----:|:-----:|:-----:|\n||overall|batch correct|bio conserve|modal integrate|IL|NMI|ARI|ASW|cLISI|ASW|iLISI|kBERT|PCR|ASW|iLISI|kBERT|GC|PCR|\n|Ours|0.58|0.39|0.69|0.61|0.57|0.68|0.58|0.61|1.00|0.83|0.27|0.16|0.31|0.83|0.28|0.06|0.87|1.00|\n|GLUE|0.55|0.36|0.67|0.58|0.55|0.67|0.55|0.59|1.00|0.86|0.20|0.13|0.25|0.85|0.15|0.09|0.82|0.99|\n|scVI|0.49|0.49|0.58|0.38|0.53|0.50|0.31|0.54|1.00|0.90|0.20|0.32|0.53|0.76|0.00|0.00|0.46|0.70|\n|Harmony|0.33|0.29|0.48|0.18|0.45|0.35|0.16|0.44|1.00|0.76|0.17|0.11|0.12|0.51|0.00|0.00|0.40|0.00|\n\n3. Clarifications of questions\n\n* We used the **modality-shared latent embeddings** for UMAP visualization and subsequent analysis.\n* **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.\n* We effectively capture **biologically meaningful representations**: \n  - 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. \n  - 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.\n  - 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].\n  - 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.\n  - **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.**\n* 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.\n\nReference\n\n[1] Luecken, M.D. et al. Benchmarking atlas-level data integration in single-cell genomics. Nat Methods (2022)\n\n[2] Fu, S. et al. Benchmarking single-cell multi-modal data integrations. Nat Methods (2025)\n\n[3] Chen, S. et al. Integration of spatial and single-cell data across modalities with weakly linked features. Nat Biotechnol (2024)\n\n[4] Chen, H. et al. SIMBA: single-cell embedding along with features. Nat Methods (2024)\n\n[5] Stickels, R.R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with Slide-seqV2. Nat Biotechnology (2021).\n\n[6] Liau, E.S. et al. Single-cell transcriptomic analysis reveals diversity within mammalian spinal motor neurons. Nat Commun (2023)."}, {"review_id": "NXnDQrTs28", "reviewer": "Reviewer_co9u", "summary": "This paper proposes scMRDR, a generative framework based on $\\beta$-VAE for integrating unpaired single-cell multi-omics data. The method disentangles latent representations into modality-shared and modality-specific components, and incorporates isometric regularization, adversarial training, and masked reconstruction loss. The authors claim superior scalability and flexibility compared to existing methods, demonstrating improved performance on two-omics and triple-omics integration tasks.", "questions": "Why does GLUE perform well in triple-omic integration (Figure 6) but performs poorly in two-omics integration (Figure 5)?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "- Strengths\n  1. The unpaired omics integration problem  is well motivated. scMRDR improves the multi-omic integration in a scalable way.\n  2. scMRDR achieves very competitive results across multiple metrics, comparable to strong baselines.\n- Weaknesses\n  1. It is inappropriate to call a dataset of 69,727 + 54,844 cells \"atlas\"-level. I understand this Section 4.3 shows the scalbility of the methods, and many other baselines could not process this number of cells, but it falls short of true atlas scales (at least at millions). This section overstates the difficulty of the scalability benchmark, ignoring the more complex multi-assay scenarios that current atlas efforts involve. Similar methods, e.g. MultiVI [1], have multi scRNA-seq assay benchmark.\n  2. Although ablation shows each loss component is essential to model performance, the loss weights are non-trivial and not systematically characterized. The selection of hyperparameters is finetuned for tasks (Appendix A.2, page 13).\n\n[1] Ashuach, Tal, et al. \"MultiVI: deep generative model for the integration of multimodal data.\" Nature Methods 20.8 (2023): 1222-1231.", "was_revised": true, "final_justification": "- The rebuttal has clarified my concerns, including the GLUE benchmark and significance of the method\n- The method was well motivated to solve the unpaired multi-omic integration task\n- As shared among reviewers, the novelty is limited to the combination of beta-VAE and the use of isometric loss and adversarial training", "rebuttal": "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.\n1. On the \"atlas\" scale\n\n* 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. \n* Meanwhile, we believe this does not diminish the **significance** of our method, because \n  * (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; \n  * (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**.\n2. On the hyperparameters\n\nBased on the original ablation experiments, we conducted experiments with a range of **different hyperparameter combinations** on the regular-scale two-omics dataset. \n* 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.\n* 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.\n### Performance under different hyperparameter configurations\n|beta|gamma|lambda|overall score|batch correct|bio-conserve|modal integrate|notes|\n|------|-------|--------|-------|---------------|--------------|-----------------|----------------|\n|2|5|5|0.66|0.52|0.74|0.70||\n|2|7|5|0.65|0.54|0.69|0.72||\n|2|5|3|0.65|0.55|0.69|0.71||\n|2|2|2|0.65|0.50|0.72|0.70||\n|2|5|7|0.65|0.49|0.70|0.73||\n|2|3|5|0.65|0.47|0.71|0.74||\n|2|1|5|0.64|0.49|0.68|0.75||\n|3|5|5|0.64|0.48|0.71|0.71||\n|4|5|5|0.64|0.47|0.71|0.72||\n|2|10|5|0.64|0.52|0.68|0.71||\n|1|5|5|0.62|0.50|0.67|0.68|beta=1|\n|2|5|0|0.61|0.53|0.69|0.60|no adversarial|\n|2|0|5|0.61|0.51|0.60|0.72|no isometric|\n|1|0|0|0.59|0.48|0.63|0.66|baseline|\n\n3. On the performance of scGLUE in section 4.3\n\nWe apologize for any misunderstandings caused by the previous presentation. In Section 4.3, the reasons for the lower metric values of GLUE include:\n* **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.\n* **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**.\n* 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**.\n### Performance of GLUE in large-scale two-omics integration\n||overall score|batch correct|bio-conserve|modal integrate|\n|----------------------|---------|---------------|--------------|-----------------|\n|Ours|0.60|0.56|0.62|0.62|\n|GLUE(LSI+NB+hvg)|0.55|0.55|0.59|0.49|\n|GLUE(LSI+NB)|0.53|0.54|0.58|0.46|\n|GLUE(LSI+Normal+hvg)|0.51|0.51|0.54|0.46|\n|GLUE(LSI+Normal)|0.48|0.51|0.48|0.44|\n|GLUE(PCA+Normal)|0.45|0.48|0.47|0.39|\n|GLUE(PCA+NB+hvg)|0.45|0.48|0.48|0.37|\n|GLUE(PCA+NB)|0.44|0.47|0.47|0.37|\n|GLUE(PCA+Normal+hvg)|0.43|0.46|0.42|0.39|\n\nReference\n\n[1] Fu, S. et al. Benchmarking single-cell multi-modal data integrations. Nat Methods (2025)\n\n[2] Khemakhem, et al. Variational autoencoders and nonlinear ica: A unifying framework. International conference on artificial intelligence and statistics (2020)"}, {"review_id": "Chnq6n6epQ", "reviewer": "Reviewer_rgSu", "summary": "This paper introduces scMRDR, a generative framework for unpaired single-cell multi-omics integration. The model combines several established ideas: it factorizes the latent space into modality-shared and modality-specific components via a β-VAE; aligns the shared latents using an adversarial objective; preserves biological structure using a novel isometric loss; and handles missing features through masked reconstruction. The framework is modality-agnostic, scales to large datasets, and is evaluated across three integration settings, including a triple-omics scenario and a 125k-cell atlas-scale benchmark.", "questions": "Clarify novelty relative to scTFBridge, scMaui, and InClust+: These methods also disentangle shared and specific latent spaces, and handle missing data through masking or PoE. Please articulate what distinguishes scMRDR beyond combining existing strategies.\n\nExplain GLUE’s underperformance: The results shown for GLUE are much lower than expected based on its original paper and follow-ups. Was GLUE tuned properly (e.g., were feature graphs provided)? A sensitivity analysis or clarification would help.\n\nReport raw scIB metrics: Normalized scores across models introduce instability depending on which methods are included. Please provide raw metrics or at least supplement the current tables with them.\n\nWhy exclude totalVI as a baseline? Even if it assumes paired data, totalVI is a standard method for multimodal integration and would serve as a strong point of reference.\n\nDemonstrate downstream impact: Can you show whether scMRDR’s integrated latent improves biological tasks beyond mixing and clustering (e.g., improved classification, rare population detection, or gene regulation inference)? This would make the model’s practical benefits clearer.", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 1, "originality": 2, "strengths_and_weaknesses": "The paper is well-written and enjoyable to read. It addresses a relevant and technically challenging problem and provides a thoughtfully engineered solution. The authors successfully integrate a combination of useful techniques - latent space separation, adversarial alignment, structure-preserving regularization, and masked losses - into a scalable, flexible framework for unpaired integration. The use of an isometric loss to preserve intra-modality structure is a novel and effective addition, and the masked loss correctly handles missing features without requiring strong assumptions or imputation. The model’s scalability is also convincingly demonstrated.\n\nHowever, the overall degree of novelty is more modest than the paper suggests. While each component is justified and works well in practice, the key ideas have been explored in prior work. scTFBridge, scMaui, InClust+, and scCross all implement variations of modality-specific/shared latent decomposition, adversarial or PoE-based alignment, and masking for missing data. scMRDR improves on these by combining them more cleanly, but it is not clear whether the combination leads to fundamentally new insights or just better engineering. The use of β-VAE is a welcome inclusion, but not unprecedented. The isometric regularization stands out as the most novel component and is likely responsible for the model’s strong performance on biological conservation metrics.\n\nThe empirical results are competitive and include both large-scale and multi-modal integration, which is commendable. That said, significant concerns remain. The poor performance of GLUE is surprising and warrants clarification. Baselines such as totalVI are missing, despite being widely used and relevant for comparison. The scIB metrics (which should be cited!) should not be normalized before aggregation, as this makes them unstable to adding bad models. Finally, the evaluation focuses almost exclusively on embedding quality and integration metrics; there is no demonstration of downstream utility on real tasks (e.g., differential expression, trajectory inference, or regulatory discovery), which would help contextualize the value of improved integration.\n\nIn sum, this is an interesting contribution that addresses integration rigorously and at scale, and incorporates an architectural addition (isometric loss), however requires some revisions. The main critique is not about correctness or utility - but that the paper overclaims novelty relative to a field where many of the individual ideas have appeared in recent concurrent work, which questions the significance of this work.", "was_revised": true, "final_justification": "- The rebuttal clarified key concerns, particularly around GLUE baseline, scIB metrics, and added spatial transcriptomics results.\n- These additions improve the paper’s clarity and demonstrate biological utility.\n- However, the main concern, limited conceptual novelty, remains largely unresolved.\n- The method combines existing ideas (e.g., β-VAE, adversarial training) in an effective but incremental way.\n- I agree with other reviewers that the paper is well-executed but overstates its novelty.\n\nUpdated score: 4, acknowledging improved presentation and practical value.", "rebuttal": "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.\n\n1. Novelty compared to other disentanglement methods\n\nAlthough 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.\n- **scTFBridge** uses a disentangled hierarchical VAE but requires **fully paired data** for training and is restricted to **dual-modality** integration (due to contrastive learning).\n- **scMaui** leverages variational product-of-experts autoencoders and adversarial learning, but also limits in **paired data**.\n- **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**.\n\nIn contrast, the innovation of **our method** lies in：\n- 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**.\n- 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.\n- 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.\n\n2. GLUE's performance in section 4.3\n\nThe comparative method GLUE demonstrates good performance in Sections 4.2 and 4.4, but is significantly lower in Section 4.3. This is because:\n* **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.\n* **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**.\n* 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**.\n### Sensitivity analysis of GLUE in large-scale two-omics integration\n||overall score|batch correct|bio-conserve|modal integrate|\n|----------------------|---------|---------------|--------------|-----------------|\n|Ours|0.60|0.56|0.62|0.62|\n|GLUE(LSI+NB+hvg)|0.55|0.55|0.59|0.49|\n|GLUE(LSI+NB)|0.53|0.54|0.58|0.46|\n|GLUE(LSI+Normal+hvg)|0.51|0.51|0.54|0.46|\n|GLUE(LSI+Normal)|0.48|0.51|0.48|0.44|\n|GLUE(PCA+Normal)|0.45|0.48|0.47|0.39|\n|GLUE(PCA+NB+hvg)|0.45|0.48|0.48|0.37|\n|GLUE(PCA+NB)|0.44|0.47|0.47|0.37|\n|GLUE(PCA+Normal+hvg)|0.43|0.46|0.42|0.39|\n\n3. raw scIB metrics\n\nWe apologize for the widespread misunderstanding caused by our previous presentation. \n* 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)\n* we attached the original unscaled metrics in the appendix (Table 2). We also mentioned that in the captions of Figures 4, 5, and 7.\n* 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**)\n\n4. totalVI as a baseline\n\nAs 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. \n\nIn **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.\n\nRelevant 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).\n\n5. downstream impact\n  - We added an additional downstream analysis: **spatial location imputation** of scRNA and scATAC.\n  - 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.\n  - 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].\n  - 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.\n  - **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.**\n\nReference:\n\n[1] Khemakhem, et al. Variational autoencoders and nonlinear ica: A unifying framework. International conference on artificial intelligence and statistics (2020)\n\n[2] Fu, S. et al. Benchmarking single-cell multi-modal data integrations. Nat Methods (2025)\n\n[3] Chuxi X. et al. Benchmarking multi-omics integration algorithms across single-cell RNA and ATAC data, Brief in Bioinfo (2024)\n\n[4] Zhang, M. et al. Spatially resolved cell atlas of the mouse primary motor cortex by MERFISH. Nature (2021).\n\n[5] Stickels, R.R. et al. Highly sensitive spatial transcriptomics at near-cellular resolution with Slide-seqV2. Nat Biotechnology (2021).\n\n[6] Liau, E.S. et al. Single-cell transcriptomic analysis reveals diversity within mammalian spinal motor neurons. Nat Commun (2023)."}]

Author rebuttal:

Meta-review: Summary
This paper introduces scMRDR, a generative framework for integrating unpaired single-cell multi-omics data (e.g., RNA, ATAC, spatial). The model disentangles shared vs. modality-specific representations via a β-VAE, adds adversarial alignment for cross-modality consistency, and introduces an isometric regularization loss to preserve intra-modality structure. A masked reconstruction loss supports incomplete features. The framework is modality-agnostic and demonstrated on tasks including two-omics integration, triple-omics alignment, and large-scale (125k cells) integration, as well as downstream spatial transcriptomics analyses (e.g., imputing spatial locations and detecting spatially variable genes).

Strengths
- Addresses an important and technically challenging problem: unpaired multi-omics integration.
- Provides a well-engineered framework that combines disentanglement, adversarial alignment, and masked reconstruction. The isometric loss is a distinct and effective contribution, helping preserve biological structure (similar ideas exist, e.g. PHATE, but this formulation is novel in this context).
- Demonstrated convincingly on multiple tasks (two-omics, triple-omics, large-scale datasets, and spatial transcriptomics downstream applications). The paper signals clear domain expertise and strong empirical execution.

Weaknesses / Areas for Improvement
- Conceptual novelty is modest, as many components (disentanglement, adversarial alignment, masking) exist in prior work; the main originality lies in the isometric regularization.
- Evaluation focuses on integration benchmarks; broader downstream biological utility (e.g. regulatory discovery, trajectory inference) could strengthen the contribution.

Decision Rationale
Reviewers converged on a positive assessment: the paper is technically sound, clearly presented, and addresses a significant challenge with a carefully designed and scalable framework. While novelty is incremental, the isometric regularization is original and impactful, and the framework convincingly outperforms relevant baselines. The rebuttal clarified concerns around baseline tuning and metrics, and additional downstream analyses further strengthened the case. On balance, the strengths outweigh the weaknesses, and the paper is recommended for acceptance.

Reviewer Discussion
- All reviewers engaged with the rebuttal and raised their scores.
- Consensus: strong execution, modest novelty, but overall positive evaluation.
Decision: Accept (spotlight)