SAVE: A Generalizable Framework for Multi-Condition Single-Cell Generation with Gene Block Attention
Authors: Jiahao Li
Jiayi Dong
Peng Ye
Xiaochi Zhou
Haohai Lu
Fei Wang
Venue: ICLR 2026 Poster (2026)
Keywords: generative model
single cell
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Modeling single-cell gene expression across diverse biological and technical conditions is crucial for characterizing cellular states and simulating unseen scenarios. Existing methods often treat genes as independent tokens, overlooking their high-level biological relationships and leading to poor performance. We introduce SAVE, a unified generative framework based on conditional Transformers for multi-condition single-cell modeling. SAVE leverages a coarse-grained representation by grouping semantically related genes into blocks, capturing higher-order dependencies among gene modules. A Flow Matching mechanism and condition-masking strategy further enhance flexible simulation and enable generalization to unseen condition combinations.  We evaluate SAVE on a range of benchmarks, including conditional generation, batch effect correction, and perturbation prediction. SAVE consistently outperforms state-of-the-art methods in generation fidelity and extrapolative generalization, especially in low-resource or combinatorially held-out settings. Overall, SAVE offers a scalable and generalizable solution for modeling complex single-cell data, with broad utility in virtual cell synthesis and biological interpretation.

Published as a conference paper at ICLR 2026
SAVE: A GENERALIZABLE FRAMEWORK FOR MULTI- CONDITION SINGLE-CELL GENERATION WITH GENE
BLOCK ATTENTION
Jiahao Li Jiayi Dong Peng Ye Xiaochi Zhou Haohai Lu Fei Wang" College of Computer Science and Artificial Intelligence, Fudan University Shanghai Key Laboratory of Intelligent Information Processing, Fudan University (lijiahao23, jiayidong21, pye24, xczhou24, hhlu24) ) @m. fudan. edu.cn, en, wangfei@fudan edu. cn
ABSTRACT
Modeling single-cell gene expression across diverse biological and technical condi- tions is crucial for characterizing cellular states and simulating unseen scenarios. Existing methods often treat genes independent tokens, overlooking their high- level biological relationships and leading to poor performance. We introduce SAVE, a unified generative framework based conditional Transformers for multi-condition single-cell modeling. SAVE leverages a coarse sonseegrained repre- sentation by grouping semantically related genes into blocks, capturing higher- order dependencies among gene modules. A Flow Matching mechanism and condition-masking strategy further enhance flexible simulation and enable gen- eralization to unseen condition combinations. We evaluate SAVE on range of benchmarks, including conditional generation, batch effect correction, and per- turbation prediction. SAVE consistently outperforms wate-of-the-as methods in generation fidelity and extrapolative generalization, especially in low-resource combinatorially held-out settings. Overall, SAVE offers scalable and gen- eralizable solution for modeling complex single-cell data, with broad utility virtual cell synthesis and biological interpretation. Our code publicly available https: ttt.ttgtt...../////// com fdu seluu-wat wangfeil lab/ sc-sccssse save
INTRODUCTION
The rapid expansion of tightthroughput single-cell RNA sequencing (scRNA-seq) technologies provides unprecedented opportunities to computationally model and simulate diverse cellular states under complex experimental conditions Kolodziejezyk et al. : [Svensson et al. (2018): Jovic et al.] (2022). Generative models that can predict gene expression profiles under unseen combinations of covariates such as cell type, disease state, and perturbation can greatly reduce experimental costs and accelerate biological discovery.
Variational Autoencoders (VAEs) have become the foundation of many generative frameworks in single-cell omics, with L et al. (2018) being notable example. While effective in learning latent representations and enabling batch correction and imputation, such models typically assume simple architectures and limited in their ability model complex, combinatorial interactions among multiple external conditions. Addressing this limitation is crucial for simulating realistic cellular responses in multi-conditional settings Luecken al. (2024).
To model condition-dependeet gene expression patterns at scale, recent approaches have adopted Transformer-basee architectures, representing cells gene token sequences and conditions as condition tokens Cui et al. (2024); Bian et al. (2024). These so-called "foundation models" rely on masked modeling objectives to capture the relationships between genes and covariates. However, they face several fundamental challenges: (I) they assume a flat, token-level view of genes, neglecting biological structures such as gene modules or pathways; (2) they fail model the global expression distribution, focusing primarily on non-zero values and ignoring the informative zero inflation inherent
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in scRNA-scq data Qiu 2020); and (3) they typically not integrated into a generative framework capable sampling from the learned conditional distribution.
We draw inspiration from masked generative modeling in computer vision, such Chang al. (2022), which demonstrates that unordered data can be effectively modeled using coarse-graine representations like image patches. Gene expression data shares key properties with images in this context-it is high-dimensional, sparse, and inherently unordered. This suggests that a similar coarse-graining strategy, modeling the level of gene blocks' rather than individual genes, could prove highly effective.
However, key challenge arises: unlike pixels, which are grouped by spatial proximity, genes lack natural local structure. To overcome this, we propose forming blocks based on semantic similarity. We leverage Large Language Models (LLMs), pre-trained on extensive text corpora, extract rich features from the comprehensive gene descriptions in the NCBI database. Genes exhibiting high semantic similarity are then aggregated into blocks. These blocks serve as coarser-graines tokens, upon which we apply attention mechanism to learn the complex relationships among them.
In this work, we propose SAVE (Single-cell Gene Block Attention-based Variational gEnerative framework), a unified framework for conditional single-cell data generation and integration. SAVE integrates the latent space structure of VAEs with coarse-grained Transformer that attends over meaningful gene blocks, effectively capturing high-order dependencies. To enhance conditional generation, SAVE employs Flow Matching, enabling simulation under complex, unseen condition combinations.
Our main contributions are summarized as follows:
We introduce Gene Block Attention, a attention mechanism that captures high-order rela- tionships among blocks of genes.
We develop masked modeling strategy Flow Matching and VAE to enhance SAVE's ability to learn the conditional distribution of cell states.
We demonstrate that SAVE achieves state-of-thh-ar performance on multiple tasks, in- cluding batch alignment, perturbation prediction, and simulation under unseen condition combinations.
RELATED WORK
2.1 GENERATIVE MODELING FOR SINGLE-CELL DATA
Variational Autoencoders (VAEs) have been widely adopted for modeling single-cell RNA-seq data. Notably, Lopez et al. (2018) introduces a zero-inflated negative binomial (ZINB) likelihood and encodes covariates into the latent space for tasks like batch correction and imputation. However, traditional VAE-based models primarily focus representation learning rather than flexible data generation across complex conditions Xiong et al. (2022). To improve generative capabilities, recent models have explored more expressive architectures. CFGen Palma et al., flow-based model, applies optimal connspot-guidee diffusion and classifier free guidance to model conditional distributions. Similarly, scDiffusion Luo al. (2024) combines latent diffusion with pre-trained autoencoder [Heimberg et al. (2025) and integrates condition labels via gradient-basee classifier guidance. While these approaches support conditional generation, they rely fine-grained diffusion processes and often struggle with interpretability and scalability across diverse biological contexts.
2.2 CONDITIONAL TRANSFER IN SINGLE- CELL ANALYSIS
Predicting gene expression under unseen conditions such as novel drug perturbations or disease states-is a central goal in single-cell analysis Wu et al. (2024). seGen Lotfollahi et al. (2019) addresses this using latent shift strategy in autoencoder framework, assuming linear transitions in the latent space. tr VAE Lotfollahi et al. (2020) applies Maximum Mean Discrepancy (MMD) for alignment and decodes data conditioned state labels. These methods, however, typically limited to a single type of condition. scDisInFact Zhang et al.] (2024) extends to multi-factor settings by employing multiple encoders disentangle condition-speciff and condition-invarian
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components, Nonetheless, such designs require predefined factor separation and often lack scalability to combinatorial condition spaces.
2.3 TRANSFORMER MODELS IN SINGLE-CELL LEARNING
Transformer- based models have recently gained traction in single-cell omics, mostly for representation learning. scGPT Cui et al. (2024), scBERT Yang (2022). and Geneformer Theodoris GeneformerTTeodorris tokenize gene expression using rank or discretized values, often sacrificing fine-grained quantitative information. GeneCompass Yang et al. (2024) improves upon this by combining rank and absolute expression with regression loss. Some methods directly project expression values into continuous space, with additional strategies to handle zero inflation. TOSICA Chen et al. (2023) uses gene networks to filter unreliable zeros, while scFoundation Hao et al. (2024) introduces special tokens to mask them. CellPLM Wen et al. (2023) models inter-cell relationships via a 'AE-Transformer hybrid, treating entire cells tokens. Despite this progress, most Transformer-basee focus on encoding rather than generation, and there little agreement on how best to represent gene expression in tokenized form. Incorporating biological structure (e.g., gene sets) and enabling conditional generation remain open challenges.
al. (2023)
methods
3
METHODOL.OGY
Gene Block Construction
Conditional Flow Matching Network
Deterninssoo
Optimal Cluszernaa
Conditoos with (AAS)
FoodForward
Inference
ACBLA
Layar Norm
Thick Green Line: Conditio Injection
ACULN
Gane Emboddings
Time step
((bed)
ACaLi
Layer
Generation
Token
Noky Lateet
A bi Di
N
Prior Noiee 2t
Genorated Fy
Input su RM (MeES)
Block Partisonin
Recoonetracted SCRNi sec Y
Trijectory
Restupe& Stuck
VAE (Compresion/ecoonstuooon
Nakumber of Calls ki Ganen per Block
Block Encoder
Gene Block Decoder #leconstructon
(Comprestion)
Sampling
Rpodl Twnsor
Latert Z
Reconstructed
Figure The overall architecture of the SAVE framework. The model consists of three main modules: (1) Gene Block Construction, which partitions gene embeddings into semantic blocks via Optimal Transport clustering; (2)a VAE utilizing Gene Block Attention for latent compression and reconstruction and (3) Conditional Flow Matching Network, which maps prior noise zo to generated latent distributions I by integrating conditions and time steps t via Adaptive Layer Normalization (AdaLN).
We present SAVE, unified Latent Flow Matching (LFM) framework for conditional simulation and status transformation of scRNA-seq data. To model complex gene expression profiles, SAVE introduces a Gene Block Attention backbone to capture long-range transcriptional dependencies. Furthermore, it incorporates rich contextual information, such as cell type disease state, through Adaptive Layer Normalization (AdaLN). The architecture comprises three core components: (1) A VAE Encoder with Gene Block Attention to learn robust latent cell representations from transcriptional patterns. (2) A Condition aaware Flow Matching module that leverages AdaLN to generate gene expression profiles precisely guided by condition embeddings. (3) A Condition Mask-based Training
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embeddingee (sll Published as a conference paper at ICLR 2026
strategy that unifies generation and transfer tasks by masking conditions for either the Flow Matching module or the VAE, respectively. An overview is shown Figure
3.1 GENE BLOCK ATTENTION FOR SCRNA-SEQ MODELING
1. LLM Embedding Construction
Cleanning
Gane fandion Bale
Gare keddon ribut bolegica
15586-immnsioone Embedding Vector (g)
NCBI Database
Summaar
embedding fest-enbeddling-tt
Captures biolog cal context
"Summary" Text
[Aug
Gene Block Processing (lterative Clustering)
Intraization (t+O)
gane embeddingg (ew) centroids (c]")
Compute Cost Matrix Cy (l0) - (/
Transport (Balanced Assignment)
Resest until Convergence
Conestainnte:
T1: 1g
3. Update Centroids
(e+1) Mean(C)
Input scRNA-seq Data
Transformed Data X (NxLaK) Lon--ovelapping Gone Dlocks
(NxG)
Figure 2: Overview of the Gene Block Construction process. The procedure is divided into two modules. (1) LLM Embedding Construction: Raw gene function descriptions from the NCBI database are cleaned and processed by LLM extract semantic embeddings (g:) representing robust biological contexts. (2) Gene Block Processing: An iterative clustering algorithm driven by Optimal Transport assigns G gene embeddings into L balanced. non-overlapping blocks.
Gene Block Processing. We first introduce our strategy for transforming single-cell expression profiles into coarse-grained, biologically meaningful representation. As illustrated in Figure 2. the construction of Gene Blocks consists of two main stages: Large Language Model (LLM) embedding construction and iterative clustering via Optimal Transport. First, following Chen & Zou (2024), we extract and clean "Summmry" texts from the NCBI Gene database to remove uninformative elements. These curated summaries then processed by LLM (text-embedd) -ngaeaa--------- to generate ..536-dimensional embedding vectors (g:) that capture rich biological context. Second, group these semantic embeddings into non-overlapping blocks of equal size, formulate the block assignment as an Optimal Transport problem. By iteratively computing the Euclidean cost matrix Cij- l1g, of 10. solving for balanced transport plan with uniform marginal constraints
(T1, a, T b), and updating the block centroids (0) the algorithm converges to structurally balanced functional modules. This process ultimately reshapes the input ScRNA-seq data Y into a structured tensor X, serving as the foundational input for our Gene Block Attention mechanism.
Transformer Block. Each gene block is first projected into an e-dimensional hidden space via learnable MI.P Win SAVE applies standard Transformer blocks to this representation using the following formulation:
ho XW ho E NxLx
he = h, + Attention (ttenion(LayrrNom((t))
h fy + Feedforaad((LayrNNom/ll
Here, h, denotes the input to the t-th Transformer block. Layer normalization is applied before Attention and FeedForward layers to enhance training stability and convergence.
3.2 CONDITION INJECTION VIA ADAPTIVE LAYER NORMALIZATION
To incorporate condition-specifee information, we encode all conditioning variables (c.g., batch, cell type, disease stage) into matrix S Nxd, where d, is the number of condition types. Each
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categorical condition is assigned unique index value, and apply learnable embedding obtain S E R dxd, Xe.
We employ Adaptive Layer Normalization (AdaLN) Xu et al. (2019) to inject condition-speciiic signals into the Transformer blocks. The parameters for A are derived from S as follows:
B1, 71, 02, 82 72 SWW 3, E IR Nxe
be ht + a1 AttentionAdaaLN(he, 71, 91))
(3)
h41 hy + 02 FeedForward(AdaaLN/ (2)) (dhLN 7, = Var[h] +
(4)
E[h +
(5)
Here, a, 3,7 y act as learnable scaling factors, modulating the influence condition embeddings on the sequence representation.
3.3 MASK MODELING STRATEGY
To enhance the model's ability generalize unseen conditions, introduce masking strategy. Each element in the condition matrix is masked independently with a fixed probability replaced by dedicated [MASK] token:
[MASK]
with probability p
Sij
Vi (1...., N).j (1....,d,)
(6)
Sij
with probability
This masking strategy helps the model learn robust representations by simulating missing information during flow matching.
3.4 COMPRESSION AND RECONSTRUCTION VIA VARIATIONAL AUTOENCODER
Attention Encoder with Gaussian Prior. The encoder's final output hy is flattened and projected to estimate the parameters of the latent distribution:
# = (h)WH, E RxLxx a² = (h)Wo,
(7)
o² e RRLxd
(8)
To regularize the latent space, we apply a Kullback Kullback-Leibler Leibler divergence penalty:
C. =
1)) = (- log(o>) + 0² + 12 -1)
(9)
Latent codes are sampled using the reparameterization trick.
Attention Decoder for Latent Tokens. The decoder mirrors the encoder structure. We apply linear projection Din to obtain hg the initial hidden state:
h Din .h NxLxe
(10)
= Decoder(Nig (hd & hWowt
(11)
The reconstruction loss is defined as: Crecon = log L(X(X)
3.5 FLOW MATCHING FOR CONDITIONAL GENERATION
The core idea of Flow Matching is to learn a time-dependent vector field ve(2) that generates a probability path (z))nnnnct simple prior distribution Po (e.g., standard Gaussian) to the data distribution P1- The generation process is then described by the probability flow ODE: dz. uz (xx).
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Instead of learning the complex marginal vector field directly, Flow Matching regresses simpler conditional vector field uy that maps a specific noise sample 2o ~ Po to a specific data sample I1 P1- This is achieved by defining probability path between them.
We utilizes a simple yet effective Affine Probability Path, which corresponds to a linear interpolation between the noise and the data. Given random time step & [0, 1], point 2y the path is defined as:
xx (1 1)z0 + tx
(12)
This formulation defines where a particle starting æ5 should be at time reach 21 time ( 1.
The training objective is to teach a neural network, (o(x, t, f). to predict the instantaneous velocity of the particle along the path. For the affine path, this velocity, the target vector field u, is simply
the time derivative of x,
dæ d ((1 1)00 + (x1) = x1 3p
(13)
dt di
The network to takes the perturbed data z₁, the timestep and optional conditioning information с as input. It is trained to approximate ut by minimizing the Flow Matching objective, which is a Mean Squared Error (MSE) loss between the predicted vector and the ground-truth vector. The loss function is formulated as:
(14) Once the model vg is trained, can generate new samples. The generation process reverses the flow, starting from random noise sample and evolving it toward the data distribution. This is achieved by solving the probability flow ODE from 0 to using the learned network vy as the velocity field function. The ODE is defined as:
(0) poo
[llvg (x),, s) uz 1
dr.
dt (o(
(15)
with the initial condition being sample from the prior, 2y Po()). To generate sample, we solve this initial value problem. The solution at 1, denoted as ø1, is a new sample from the learned data distribution.
We also implements Classifier-Free Guidance (CFG) Ho & Salimans (002). a technique to enhance the influence of the conditioning signal y. The effective vector field during inference becomes weighted combination of a conditional and an unconditional prediction:
0 = w) vig #0( 1) + w 4,
(16)
where w is the guidance weights. This allows for controlling the trade-off between sample diversity and fidelity to the conditioning information.
RESULTS
In this section, we comprehensively evaluate SAVE across multiple tasks. In Section 4.1 begin with the introduction of the experiment setting and the implementation details. In Section 4.2 we compare it with baseline models both single-condition and multi-condition generation across three datasets, using distributional visualization for qualitative assessment and distance-basse metrics to quantiffy similarity between real and generated cells. We then assess SAVE's performance on two classical benchmarks: batch effect removal (Section 4.3) and out-of-samppl perturbation prediction (Section 4.4). Finally, we conduct ablation and robustness studies (Section 4.5) to evaluate the contribution of each model component.
4.1 EXPERIMENT SETUP
Following standard bioinformatics protocols Wolf al. (2018), the expression values for each cell were normalized to total of 10 counts and then log-tra angtrranformmd. Before being input into the neural network, the scRNA-seq data underwent max-absolute normalization, scaling all values to the range [0, 1]. The SAVE model was configured with gene block size of K 3200. The condition masking ratio was set to 0.6. Model optimization was performed using the Adam optimizer with learning rate of x 10 and weight decay of 2.5 x 10 5, All experiments were conducted GeForce RTX 3090 24GB GPU. The same set of hyperparameters was used for all experimental settings. A detailed list of model parameters is provided in Appendix Table

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4.2
CONDITIONAL GENERATION PERFORMANCE
scVI
CFCen
scDiuasion
SAVE
Foodeet
Figure 3: UMAP visualization of generative model outputs on the Heart dataset. The top row illustrates the discrepancy between the generated and real data distributions, the middle highlights different batches, and the bottom row denotes cell types.
Table I: Single conditional generation performance, Best results bolded, and second-best underlined.
PBMC3K
Dentate gyrus
Tabula Muris
Method
WD (})
MMD (L)
WD (L)
MMD (L)
WD (L)
MMD (L)
scV1
17.66
0.94
22.61
1.15
9.76
0.26
scDiffusion
22.41
1.27
22.56
1.22
7.89
0.24
CRGen
16.94
0.85
21.55
1.12
7.39
0.19
19.14
1.80
9.16
0.17
10.86
Conditional generation scenarios are categorized into three types: single-condition, dual-condition multi-platform sequencing data, and large-scale datasets with diverse expert annotations (c.g., cellx- gene Megill et al. )202T). We compared our model with VI, CFGen, and scDiffusion.
Performance on single condition datasets. We first conducted comparative experiments on datasets containing single condition: PBMC3K
PBMC3K"[conditione (conditioned cell type). Dentate gyrus La Manno et al. (2018) (conditioned on clusters), and Tabula Muris Consortium (2020) (conditioned on tissue). As shown in Table while baseline models such as CI-Gen perform competitively on the relatively simple PBMC3K dataset, SAVE demonstrates significant advantage the data complexity increases. Notably, on the Dentate gyrus dataset, SAVE dramatically outperforms all baselines, reducing both WD and MMD by more than half compared to the second-best method. On the Tabula Muris dataset, SAVE achieves the lowest MMD (0.04), indicating a highly accurate alignment with the global means of the real distribution. Although CFGen and scDiffusion exhibit strong WD scores certain metrics, their performance fluctuates across different data scales. In contrast, SAVE provides a much more robust distributional fit for complex cellular data, demonstrating that adopting gene block attention effectively captures the overall structural dependencies that simpler architectures struggle to model.
Performance dual-condition datasets. We evaluated the generative models complex multi- platform datasets conditioned on both batch and cell type, requiring the models to simultancously disentangle and learn the influence of two covariates. Table presents the quantitative results for three representative datasets (Heart Litviñuková et al. (2020). 1BMC|iisched et al. (202T), and Lung Atlas Luecken et al. (2022)). As shown in Table SAVE consistently exhibits leading performance across all three evaluated datasets, achieving the lowest WD and MMD scores and demonstrating strong scalability. scDiffusion shows competitive yet second-best results. CFGen, despite employing advanced flow matching, struggles with the dual-condition complexity, performing similarly to the baseline scVI on the Lung Atlas dataset. UMAP visualizations on the Heart dataset are presented in Figure While CFGen and scDiffusion demonstrate good fitting for the overall data distribution,
https://sati
mtmm]

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they exhibit relatively disorganized distributions for the multi-batch Ventrieular Cardiomyocyte population. In contrast, our method, SAVE, effectively distinguishes batch differences within this cell type, enabling much more accurate topological modeling.
Table 2: Dual condition generation performance.
Heart
PBMC
Lung Atlas
Method
WD (L)
MMD (4)
WD (4)
MMD (4)
(D
MMD (L)
ScVI
19.18
1.19
17.75
0.95
22.20
2.27
CFGen
12.57
0.66
17.41
0.65
28.02
1.76
scDitfusion
20.82
0,94
11.38
0.48
13.89
1.71
SAVE 8,30
0.63
5.37
0.29
4.37
1.14
Multi-condition generation performance. To evaluate the fitting of complex multi conditionll distributions, we utilized a Lung Cancer dataset (Slcset et al. (2022) characterized by five conditions: sequencing protocol, developmental stage, cancer status, cancer stage, and cell type. These conditions were mapped to 27 discrete types (see Appendix Table TT). Conditions 13 and 24, representing rela- tively smaller data subsets, were selected as the unseen test set evaluate conditional extrapolation, while the remaining conditions formed the training set. As shown in Table 15] SAVE demonstrates robust performance in capturing the complex data distribution. For the seen conditions, SAVE achieves the best WD score and matches se scDiffusion on MMD. Crucially, on the held-out unseen data, SAVE maintains the lowest WD score, indicating that its generated global distribution remains closest to the ground truth even under novel condition combinations. While scDiffusion achieves a slightly lower MMD on the unseen set, SAVE provides more balanced and accurate overall fit, Figure 4 a) demonstrates that even with limited training data, CFGen and scDiffusion generate data distributions that deviate significantly from the real data, whereas SAVE produces much precise distribution. Figure 4b)) further highlights that SAVE's generated data maintains a tighter alignment with the ground truth in the latent space.
as further supported by the visual alignments in Figure 4
Uppa
Oround
Cel b99
Figure 4: UMAP visualization of generative model performance on the Lung Cancer dataset. Panel (a) illustrates results on the seen conditions, and panel (b) shows performance on the unseen conditions.
Table 3: Quantitative evaluation of generative model performance the Lung Cancer dataset. WD and MMD for seen and unseen conditions are averaged.
Seen
Unseen
Method
WD
MMD (4)
WD (L)
MMD (L)
CFGen
16.94 +: 4.19
1.49 = 1.80
23.67 + 3.08
2.76 2.64
scDiffusion
5.27 2.14
1.06 = 1.59
5.29 1: 2.03
1.87 :: 2.31
SAVE
3.10 0.96
1.06 = 1.48
4.63 1 0.95
2.11 2.11
4.3 BATCH EFFECT CORRECTION
Batch effect correction is commonly employed to align multiple sequencing datasets, mitigating its impact on downstream analyses such as differential gene expression and gene regulatory network inference. Its effectiveness is typically assessed using metries such the biological conservation score (Bio.) and the batch correction score (Batch). The seIB score provides a comprehensive evaluation by jointly considering both biological preservation and batch mixing performance. We
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systematically evaluated SAVE three multi multi-platform scRNA-seq datasets (used in dual-condition generation task) and compared its batch correction performance against four established methods: Scanorama Hie et al. 2019), Harmony Korsunsky et al. (2019) sc scV1, and tr VAE. Across all datasets, SAVE consistently achieved the best overall integration quality, attaining the top biological conserva- tion score in three datasets and the best batch correction score in two, shown in Table Traditional methods like Harmony remained competitive, ranking top in batch correction for Heart and showing stable performance overall. In contrast, deep learning methods exhibited trade-off's: sc'II often underperformed in biological conservation, while tr VAE achieved strong batch correction but at the cost of biological fidelity. These results highlight SAVE's ability effectively disentangle biological variation from technical noise, particularly in complex heterogeneous tissue datasets.
Table 4: Batch effect correction performance of SAVE model.
Lung Atlas
Heart
PBMC
Method
Bio. (1)
Batch (1)
scIB (f)
Bio. (1)
Batch (1)
sclB (t)
Bio. (1)
Batch (1)
scIB (t)
Scanorama
0.70
0.88
0.77
0.72
0.82
0.76
0.71
0.93
0.80
Harmony
0.65
0.93
0.76
0.76
0.89
0.81
0.71
0.95
0.80
ScVI
0.58
0.83
0,68
0.66
0.81
0.72
0.47
0.78
0.59
IVA
0.69
0.90
0.78
0.75
0.83
0.78
0.75
0.91
0.82
SAVE
0.73
0.93
0.81
0.76
0.86
0.80
0.75
0.95
0.83
4.4
PERTURBATION PREDICTION PERFORMANCE
PCDRDA
ICAT
NC
BANG
Figure 5: Performance comparison between predicted and stimulated (real perturbed) data. The top row presents UMAP visualizations comparing each method's predictions to the real perturbed condition (yellow), where closer proximity indicates better prediction accuracy. The bottom row shows violin plots of the expression distributions for the most significant differentially expressed genes predicted by each method.
Drug perturbation prediction typically involves learning the effects of drug perturbations various cell types from training data and generalizing to novel cell types. We evaluate our approach on predicting IFN-3 drug perturbation data from the PBMC-IFN dataset Haber et al. (017)). As shown in Figure 5 SAVE produces predictions that most closely match the true stimulated (real perturbed) conditions, substantially outperforming other models. Among the baselines, seGEN demonstrates highly competitive performance, with their generated distributions tracking closely to the stimulated targets. contrast, trVAE's outputs tend resemble the control condition, suggesting effects. Meanwhile, scDisInFact exhibits significant
limited capacity to model deviations, likely due to optimization challenges or an emphasis on latent space alignment at the expense of accurately capturing the observed data distribution. The violin plot depicts the overall distribution of highly variable genes, and similar conclusions can be drawn.
From the perspective of quantitative analysis in Table 5 SAVE achieves average PCC exceeding 0.95 and an R² of 0.86, consistently outperforming all baselines. CellOT Bunne et al. (2023) and scGEN serve the strongest baselines, both achieving average PCC of 0.94, while VAE shows moderate performance. Conversely, MFM and scDisInFact perform the worst; notably, MFM Atanackovic al. 2025) yields predictions (average PCC 0.71) that are inferior
the

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baseline correlation between the unperturbed control and perturbed data (average PCC 0.86). We observe that for cell types with significant differences between control and perturbed conditions, such CD14+Mome and FCGR3A+Mono, SAVE yields superior prediction performance. Similar conclusions are drawn from the R² metric, indicating that SAVE is able to capture more conditional effects expression values.
Table 5: Quantitative evaluation of perturbation prediction methods on the PBMC-IFN dataset.
Dendriic
Average
PCC
(P)
PCC
PCC
PCC
(1)
PCC
PCC
20
J8
0194
01.58
0..32
0.:8
0.38
0.91
0.51
0.51
0.79
0.55%
0.34
0.86
0.66
BYAF
0196
11:66
0.82
0..99
0..3
0.50
0.90
0.78
0.97
0.96
01.83
0.:6
0.99
0.92
(190
0.68
seDstaFact
0385
01.33
0.77
0.41
0.71
0.43
0.34
0.45
0.83
0.43
0.76
0.-7
0.79
0.44
0.80
0.45
SOGEN
01955
01:55
0.94
0.90
0.95
0.77
[.91
0.53
0.92
0.35
0.96
0.89
0.95
0.54
0.84
0,85
MFM
0.75
0.60
0.77
0.53
0.56
0.08
0.70
0.49
0.70
0.49
0.72
0.51
0.72
0.51
0.71
0.46
CHIOT
0.99
0.97
0.99
0.98
0.77
0.02
0.55
0.59
0.97
0.6
0.96
0.88
0.96
0.90
0.94
0.50
SAVE
0.95
0.37
0.97
0.89
0.91
0.53
0.37
0.94
0.96
0.97
0.96
0.81
0.96
0.90
0.96
0.86
4.5 ABLATION
Ablation of gene block attention. As shown in Table removing this module leads drop in performance, particularly on the WD metric. This suggests that gene block attention helps the model capture structured relationships among genes and learn biologically meaningful representations.
Effect of gene block size. Table 7 shows the impact of block size K on generation, where a suitable K optimizes both MMD and WD. Separately, Table evaluates training efficiency under fixed 24GB VRAM limit. Compared to naive attention (K = 1), applying block attention delivers 191 speedup (e.g., 12.5 vs. 2391.2 mins), drastically reducing computational costs.
Table 7: Ablation study of gene block size.
Table 8: Training times use different block size.
Table 6: Ablation study of At- tention module.
K
L
WD (L)
MMD (L)
600
32
9.70
0.66
K
Time (min)
Setting
WD (1)
MMD (1)
1600
9.64
0.65
1
19112
2391.2 1.2
SAVE w/o Au
8.89
0.65
2400
8
8.64
0.62
1600
12
16.4
SAVE
8.30
0.63
3200
6
8.30
0.63
3200
12.5
4000
5
8.37
0.63
5600
9.0
5600
4
8.41
0.63
CONCLUSION AND LIMITATION
We present SAVE, a unified generative framework for multi-conditios single-cell modeling. By integrating generative model with conditional Transformer and incorporating knowledge-inspired gene block attention with masked condition modeling, SAVE can generate realistic cell profiles across diverse-even
iincen-conditionss Experiments on public datasets show that SAVE consistently outperforms existing methods in conditional generation, batch correction, and perturbation prediction, with strong generalization low-data and novel-condition settings. Overall, SAVE provides versa- tile tool for virtual cell synthesis and single-cell analysis, advancing generalizable and biologically grounded generative modeling.
Although our LLM-based gene block construction effectively captures high-order semantic relation- ships, inherently relies on the comprehensiveness of existing literature and database annotations. While this data-driven approach yields rich functional context for well-studied genes, it may produce less informative or noisy embeddings for poorly characterized or newly discovered genes due to sparse text descriptions. Furthermore, in contrast to manually curated, gold-standard pathway databases (e.g., MS or KEGG) that provide rigorously validated biological interactions, our unsupervised text-driven grouping is more susceptible to historical literature bias. Future iterations of the SAVE framework could mitigate this by integrating structured biological knowledge graphs or curated gene regulatory networks with the LLM embeddings.
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A CODE OF SAVE MODEL
The main code available at https:/ggghaaacccm/ddddwvvaaaaat
B FUNCTIONAL VALIDATION THROUGH CONDITION-MODULATII BLOCK ATTENTION
Model Attention Heatmap: Cell Type vs. Batch
Dominent Pathway
D11
4
3
Not Obsorved (Misinng Datal
Block 0: Regu wtenn DMAtempteted transcrittion (irancciptional Controll
D2
Block 1: Futty Acid Seta Condation (Metaroiamm
Block 2: Braddienneall Celldar Fanct one din sinlle dominant pathwry endihhed
23
3
Bluck 3: Esabiishmet of Pratoin Localitation to Pasma Membrone rino (Stucduro (Tansportt
Block 4, Adonviate Cyc Activating Protzin Coup Soupled Recestor Signaling (Signaling)
Baten Nome
D3
137
122
2H4
FR
petpergree
diuropicgts
Bnieshettal
Plrcalest
Lymphhatd
Mesutheeial
Neuronall
Haakspigret
Pertcyyte
dit diatiets
Scoeatt reak
Hestricala Card
Type
Figure 6: Condition-Modulatee Attention Heatmap across Cell Types and Batches.
To ensure the creation of balanced semantic groups, we initialized our approach by selecting 16,000 highly variable genes (HVGs) from the Heart dataset. These were partitioned into five distinct blocks. each having a fixed size of 3,200 genes. To rigorously define the biological identity of each block, we identified the top-50 "centroid genes" (those closest the embedding cluster center) and performed Gene Ontology (GO) enrichment analysis. As shown in Table 1, this partitioning successfully resulted blocks corresponding to distinct and specific biological pathways, ranging from Metabolism (Block 1) to GPCR Signaling (Block 4).
To further validate that the model dynamically leverages these defined biological meanings, we analyzed the condition-mmouulated attention mechanism within the Flow Matching transformer. Specifically, we extracted and averaged the attention weights from the final layer across all four heads to pinpoint the gene block that was "most attended" under specific biological conditions.
The resulting attention heatmap (Figure reveals that our model transcends simple statistical fitting and successfully captures canonical biological semanties:
Physiological Alignment: The model accurately identifies the distinct metabolic signature of Cardiomyocytes (both Atrial and Ventricular) by exclusively attending to Block (Fatty Acid Beta-Oxin Oeiaa-xiiaaiion.. This mirrors the heart's well-established reliance on lipids as its primary energy source.
Functional Specificity: In cell types requiring extensive environmental interaction and signaling-Such Endothelial cells and Fibroblasts the attention dynamically shifts to Block 4 (GPCR Signaling) and Block (Protein Localization). aligning precisely with their known roles in transducing extracellular signals.
Biological Filtering: Most critically, Block 2 (Broad/General Cellular Functions) is univer- sally suppressed across the entire heatmap. This demonstrates that the attention mechanism acts as an effective biological filter, autonomously learning to ignore uninformative gene groups while prioritizing functional modules for accurate generation.
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C
HYPERPARAMETER OF SAVE MODEL
Table Model Hyperparameter Configuration
optimizer
Adam W
le-4
batch size
1024
Training
weight decay
2.5e-5
epoch
200
warmup epoch
50
Model
gene block size
3200
512
64
num_dec block
3
enc_enne_____ num enc block
attention head 4
D DETAILED CONDITION DEFINITION FOR THE LUNG CANCER DATASET
Table 10: Detailed conditions of the Cancer dataset in the multi-condition experiment. "count" represents the number of cells for each corresponding condition. The Cyan background indicates the test conditions.
assay
developeentt stage
uicc_stage
count
0
10x v2
S5-yeur-old human stage
chronic obstructive pulmonury disease
Don nom-cancer
5177
GEXSCOPE technology
55-year-old stago
lung adenocarcisoms lung adenocarcinoma
2
Smart-weq2
y-ur old human stuge
IV
2240
3
10x 3'
55-year-old human stage
non small cell carcinoma.
11151
55-year-ol old stage
non cuncer
5
BD Rhapsody Whole Transcrptomee Analysis
55 5S-yeur-old human stage stage 55-ycar-old
squamous cell lung carcinoma.
III
8179
GEXSCOPE tetnoooo
squamous chromic obstructive pulmonary diseuse
7
v2
60-y old human stuge 60-year-old human stuge 60-year-old human stage year old human stage 60-year-ol old human stuge 65-year-old human stage stuge 65-ycar-old human stage year old human stuge 65-year-old human stage 65 -s-yyerr-ld old human stage stage 70-ycar-old human stage 70 old human stuge
DOm cuncer
2418
8
Smart-seq2
adenocarcinoms
IV
54
year old
lung
10
10x 3' V2
squamous cell lung carcinoma.
4497
BD Rhupwody Whole Transriptome Analysis
squamous cell carcinoma
3663
GEXSCOPE technology
squamous cell lung carcinoma
III ov
4722
10x V2
chrocic obstractive pulmonarr discase lung adenocurcinoma
bon-cancer
355
year old
15
BD Rhapsedy Whole Transcriptome Analysis
lung adenocarcinoms
1 III
2090
10x 3'
adenocarcinoma
6102
GEXSCOPE technologyy
lung adenocareisoms normal
III of
1394
18
10x 3' v2
non non-cancer
7825
GEXSCOPE technology
65-year-ol
squamous lung
10x 3' V2
chronic obstructive pulmonary discase adenocarcinoma
non-cancer
2064
3' v2
BD Rhapsody Whole Transcriptome Analysis
70-year-old human stage 70 70-yeur-olh old human stuge slage 70-ycar-old human stage
lung adenocarcisoms
13604
23
BD Rhupsody Whole Transrrptome Analysis
squamous cell lung carcinoma
90.56
Smart-seq2
70-year-old
squamous
25
10x 3' vl
squamous czll lung carcisona
956
Smart-seq2
70-yeur-ole human
squamous cell carcinoma
III
867
E PERTURBATION PREDICTION PROCEDURE AND EVALUATION
We obtained data for evaluating perturbation prediction using a Python script available at com/the s code/DattDownloaae py, with parameters 'pbmc'. The training and validation datasets for PBMC IFN-3 were merged for our evaluation.
For perturbation prediction, we employed leave-one-out approach where each cell type was iteratively selected as the test set, with the remaining cell types serving as training data. SAVE trained this data, with the perturbation condition input into the AdaCond module. Post- training, SAVE predicted the stimulated test data for comparison with the true stimulated data. We assessed the similarity between average gene expressions using Coefficient of determination R?
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Mean Squared Error (MSE), and Pearson Correlation Coefficient (PCC). R² and MSE were calculated using sci,it-learn, while PCC was computed using SciPy.
We compared SAVE with trV, scDisInFact, and scGEN.
seGEN: Utilizes vector arithmetic in the latent space of its autoencoder for perturbation response prediction. We followed the tutorial at https::/ en http:////ttttraaaaeo//e/eeerauap potertiiiiiiooeeiiiiioiio html.
hedocs io/
trVAE: Employs its networkpredictt) function with the perturbation condition to predict perturbation responses.
seDisInFact: A deep learning method that disentangles latent factors to generate gene expression data. We implemented following the tutorial at https::// com/ ZhangLabGT/scCDD InFact.
F EVALUATION OF BATCH EFFECT CORRECTION
We conducted batch effect correction experiments using five multi-batch datasets: Mouse, PBMC, Pancreas, Heart, Lung. These datasets were obtained from the following sources:
http://///tteee..ooo...///////// Autaafttiibbceeeega/aa/////arrrr /view22spp=shriing
Mouse:
PBMC: httph//wwwaaaaaa.aa////////////a
Panereas: h|g
Heart: http::///ttttticcoo///eaaaaattts
subsampleed_20k.hag
Lung Atlas: httph:tp////...... /ttpa////a///////oooooo///////// 400.
6084
To evaluate batch effect correction, we compared SAVE with four methods: Harmony, Scanorama, VI, trV. We followed the default pipelines for each method to perform integration across all datasets. The implementation details for each method are as follows:
scVI: The integrated molecular space
profile was
obtained
using the
function.
Harmony: We utilized the Python package available https: htttps://gthutte www.thhub.comm slowkow / htarooyym........ Harmony employs a fast and effective algorithm to project various batch data into common space.
Scanorama We employed the same function used for latent integration, scanorama.cores correct wwtprrccceereeccpyllllelle scanpyladatas, return return_dimmen (iir_ddiredd=rre) The corrected adatas.X used as the integrated molecular space profile.
trV::: We utilized the predict)) function to transfer the input ScRNA-seq data to specific batch. For scIB evaluation, we applied this function transfer input data each batch and calculated the average of transferred scIB scores as the final seIB score.
For visualization, we employed the UMAP algorithm using default parameters from the Python package ScanpyWoll Wolf et al. (2018). Clustering results were annotated with the cell type and batch information from the raw data. We utilized the 50-dimensional PCA features the corrected data for clustering.
The batch effect correction performance are evaluated using 10 well-established metrics from the seIB package with default parameter/LLeccen et al. (2022). We used the overall score, which is the average of batch correction and bio bio-information conservation performance, as the final evaluation metric.
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Table 11: Ablation of condition mask on VAE perturbation prediction.
Method
PC
18
88
pCC(t)
28
SAVT
1151
103
023
0130
SAVE
0.98
0.7
037
0.89
0.1
053
0,97
0.94
0.99
0.9
0.96
0.11
0.96
0.90
0.96
0.96
G ABLATION OF CONDITIONAL MASK MODELING.
To test the effectiveness of conditional mask modeling, ablated this component by directly feeding condition labels without masking. As shown in Table [1 this led to marked decrease in generalization performance unseen condition combinations. The results suggest that conditional masking acts as regularizer, encouraging the model to learn more transferable condition embeddings, which in turn improves extrapolation.
H GENERATION PERFORMANCE
H.1
GENE LEVEL PERFORMANCE
Table 12: Quantitative evaluation of different models across three datasets (Best: bold, Second best: underline).
Model
PEMC3K
Dentate
Muris
11a
PCC
It
scVI
0.07 1. 0.14
0,93 1. 0,12
0.87 1: 0.22
0.00 1: 0.00
0.99 1. 0.01
0.99 0.01
0.07 1 0.03
0.98 1. 0,01
0.30 1: 0.32
0.14
1,00
Diiffasion
0.11 0.12
0.86
1 0.10
0.73
1: 0.17
0.00
1: 0.00
0.99
0.01
0.98
1: 0.01
0.01
0.01
0.99 1 0.01
0.94 1: 0.09
SAVE
0.08 + 0.18
0.93
+ 0.12
0.84
+ 0.27
0.00 + 0.00
0.99 0.01
0.97
0.02
0.00
0.00
0.99 + 0.01
0.95 + 0.05
Table 13: Quantitative evaluation of different models across three new datasets (Best: bold, Second best: underline).
Lang
Model
MSE
PCC
MSE
PCC
MSE
PCC
0:07
0.14
1.45
-0.57
CFGcn
0.04 2: 0.09
0.87 = 0.18
0.75 0.32
0.06 0.06
0.87 2: 0,08
0.75 0.15
0.14
0.58 1 0.20
0.17 0.52
scDiffuion
0.02 + 0.04
0.87 = 0.14
0.79 1 0.23
0.03 0.03
0.93 4: 0.06
0.86 = 0.10
0.03
0.02
0.65 4: 0.14
0.35 = 0.24
0.11
0.84
H.2 VISUALIZATION OF SINGLE CONDITION PERFORMANCE
Figures
S and
show the UMAP visualizations of the generative model on the single-condition https: //st jal ab org/ seurat/ httpaaattttttttsteeeeeeeteeeeeet tites/ppmn3.. pkmc3k tutorial
datasets PBMC31
html
Dentate Gyrus La Manno et al. 2018). and Tabula Muris Consortium (2018), respectively.
H.3 VISUALIZATION OF DUAL CONDITION PERFORMANCE
Figures 10 and show the UMAP visualizations of the generative model on the dual-condition datasets Mouse endocrinogenesis, PBMC, Pancreas and Lung Atlas, respectively.
H.4 MULTI-CONDITION GENERATION PERFORMANCE
Setup. For the Lung Cancer dataset Salcher al. 2022 we selected samples corresponding to devel- opmental ages from 55 to 75 years, at 5-year intervals. These samples were divided into 27 categories, each containing heterogencous cell types, yielding a total of 618 unique conditions. We designated conditions 13 and 24, characterized by smaller data volumes, as the test set, while the remaining data served as the training set. Five condition categories were utilized: assay, development stage, disease, uice stagee and cell type. Given that scVI is not designed to handle unknown conditions, comparison here is restricted to CFGen, scDiffusion, and SAVE. CFGen uses classifier-fre guidance for condition combination, whereas seDiffusion employs classifier guidance.
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Table 14: Quantitative evaluation of models on Seen and Unseen datasets (Best: bold, Second best: underline).
Seen
Unseen
Model
MSE
PCC
R
MSB
PCC
CFGen
0.28 +: 0.25
0.73 0.17
0.48 = 0.33
0.62 + 0.41
0.56 + 0.16
0.20 = 0.30
scDiffusion
0.03 +: 0.03
0.85 + 0.14
0.72 = 0.27
0.05 + 0.05
0.81 + 0.14
0.63 = 0.27
SAVE
0.01 + 0.02
0.94 0.07
= 0.14
0.04 0.03
0.85
0.08
= 0.14
ScVI
CFGen
scDiffusio
SAVE
type
type
LIAVSS
Sensreted
Sround Trus
DIRPPT
UMAPT
DRAPT
UMAPP
type
type
type
Menocyles
Figure 7: Generation results of the generative models on the PBMC3K dataset, visualized using
UMAP.
8CVI type
CFGen lype
scDiflusion type
SAVE
typи
UIAAPE
UMAF1
UM4411
UMAPI
UMAF1
cell type
cell type
cel type
Dell type
CA CA1 Bub
CA2-3-4
GixiPing
LIMAPE
immörante1
ImmG-anite?
@ Ni11
OPC
RaduGua
Radw
Figure 8: Generation results of the generative models on the Dentate gyrus dataset, visualized using
UMAP
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SAVE
Ippe
tyze
hyp
type
Genarisd
Broud Truft
LWWAP1
UWAPI
UM4F1
celLiyze
Biddeer
Marmay,
Sprecn
eives Wede
Thyers
Love
Treque
elurg
Figure 9: Generation results of the generative models on the Tabula Muris dataset, visualized using UMAP
CFGen
scDiffusion
SAVE
UMAP2
batch
batoh
baton
balon
12.5 troferenze)
13.5 (reference)
14.5 treference)
15.5 tquery)
UMAPI
UMAF1
UMAPI
UMAP
Reta
Figure 10: Generation results of the generative models on the Mouse endocrinogenesis dataset, visualized using UMAP.
19

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Published as a conference paper at ICLR 2026
ScVI
CFGen
scDiffusion
SAVE
Tuzt
basth
201hh
buzch
Degan U
sumpll
sxmple
COS: Toch
B.010 Rodis
8:0015 Meremsin
USAPT
Figure 11: Generation results the generative models on the PBMC dataset, visualized using UMAP.
scV1
CFGen
scDiffusion
SAVE
typw
UMMPI batch
bateh
batch
batch
e ceiseg caltegt e fluddggne e inDeppt InDeggo
inDrpp
HDDrpp
starter
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UMAPI
UMMP1
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type
8 activoted atellate alphs
beta
delta
ducial
endothecial
opsilon
quieecent, stelats
UMAP1
UMMPI
UMAP1
UMMP
Figure 12: Generation results of the generative models the Pancreas dataset, visualized using UMAP.
20

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Published as a conference paper at ICLR 2026
scVI hpp
CFGen tyce
scDittusion
SAVE
Ippa
UMAPP
LMMPP
USAP1
LSMPP
batch
buish
balch
buish
0.00
835
IMAPP
UMAPP
LSAAP1
apa
opp
Jyce
Scal
Macrophage
Soax
Must call
Rocx
Haurreed high
No
Eresitslur
TTMK
lonocyass
Teae
DSAPP
LMAPT
DRAPT
LSAPPT
Figure 13: Generation results of the generative models on the Lung Atlas, visualized using UMAP.
Results. We showcase the performance of the generative model the multi-condition lung cancer dataset in Table [5] We also provide comparisons with ablation studies that omit the attention mechanism and the latent mask. The SAVE model consistently demonstrates superior performance over other compared methods.
I BATCH EFFECT CORRECTION
In this section, we present detailed metrics for batch effect correction. These encompass bi- ological information preservation metrics Adjusted Rand Index (ARI) Normalized mutual in- formation (NMI,, Average silhouette width (ASW) and batch effect removal metrics ASW batch, Principal component regression score (PCR), Graph Connectivity (graph conn). De- tailed metrics can be found tt readthbooscccccccoooco http:/s../oen/nettt//eeeaee en/ www.lattetttttaea /api http/ppp.mmmmmmmmmmm
batch--correttion-neerrr SAVE demonstrates good performance across all these metrics.
PERTURBATION PREDICTION PERFORMANCE
J.1 WD AND MMD OF PERTURBATION PERFORMANCE
J.2 MSE AND DISTRIBUTION OF TOP 5 DEGS ON PBMC IFN-8
In Table 20 we present the Mean Squared Error (MSE) between the gene expression of predictions from perturbation prediction methods and those of the ground truth PBMC IFN-3. In Figure 14] we show the distribution the top 5 differentially expressed genes (DEGs) predicted by perturbation prediction methods. On both evaluation metrics, SAVE's prediction is closest to the ground truth.
21

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Published as a conference paper at ICLR 2026
Table 15: Performance of generative models for each condition the Lung Cancer dataset.
CFGen
scDiffusion
SAVE
Condition
WD (L)
MMD (4)
WD (L)
MMD (L)
WD (L)
MMD (4)
0
20.89
1.34
4.87
0.63
2.66
0.67
15.36
1.86
5.33
1.45
3.24
1.5
16.08
1.04
10.31
1.2
2.54
0.75
13.29
0.68
3.76
0.37
2.56
0.52
4
17.97
1.5
8.47
1.24
6.47
0.97
5
16.09
1.03
4.97
0.66
2.97
0.77
6
15.65
2.51
6.95
2.12
4.1
1,97
23.28
1,27
4.38
0.46
2.66
0.59
14.49
2.13
11.76
2.38
3.35
1.68
9
12.8
0.53
4.51
0.31
2.59
0.43
10
13.36
0.83
4.43
0.55
2.54
0.69
11
16.75
1.49
4.68
1.04
2.85
1.12
12
19.6
2.73
7.91
2.22
3,42
1.97
13
24.15
2.83
5.39
1.9
4.6
2.15
14
13.34
1.67
4.12
1.28
2.88
1.36
15
14.96
1.26
4.87
0.89
2.8
0.98
16
14.51
0.73
4.63
0.44
2.8
0.55
17
18.47
3.53
5.87
2.76
3.31
2.67
18
21.02
1.51
5
0.77
2.67
0.83
19
20.83
2.43
6.55
1.77
3.05
1.68
20
22.28
2.00
5.03
1.19
2.94
1.21
21
18.83
5.8
5.13
4.7
4.28
4.72
22
16
1.04
3.74
0.6
2.8
0.75
23
15.32
0.72
4.65
0.4
2.75
0.51
24
20.89
2.38
4.7
1.68
3.36
1.86
25
14.01
2.12
5.07
1.69
2.79
1.68
26
20.12
0.58
4.21
0.2
2.16
0.32
Average
17.42
1.76
5.60
1.29
3.15
1.29
Table 16: Detailed scIB scores for batch effect correction methods the PBMC dataset.
ARL
ASW_Jabel
JaW_label/ouch
graph_comm
2V2
avg
Scunarama
0.8053
0.7521
0.5833
0.8989)
0,5067
0.9577
0.7138
0.9233
0.7996
Hamoony
0.8008
0.7605
0.5541
0.9243
0.6959
0.9686
0.2051
0.9464
0.9016
scVI
0.5614
0,2905
0.5594
0.7678
0,7855
0.4704
0.7767
0.5929
SAVE
0,8637
0.7952
0.595%
0.9128
0.4996
0.9668
0.7516
0.9498
0.8309
Table 17: Detailed seIB scores for batch effect correction methods on the Lung Atlas dataset.
8MI cluster/abe)
ART closterlabe)
ASW Sabel
ASW Jabe//otch
PCR buich
bno buicc
selb
Hammony
0.7727
0.5973
0.5741
0,9039
0.3605
0.9472
0.6:18
0.9255
0.759
seVI
0.7358
0.4599
0.5478
0.7851
0.0557
0.8846
0.5805
0.8348
0.6822
IVAE 0.7042
0.6462
06355
018265
0,4414
0.9826
0.6919
0.9046
0.777
SAVE
0,8285
0.7340
0.6395
0.2134
0.9926
0.7340
0.9309)
0.8128
Table 18: Detailed seIB scores for batch effect correction methods on the Heart dataset.
NML XML clusterlahel
ARL clusterlahel
ASW lahel
ASW Jabel/harch
PCR botch
graph,ccom .oon
BVg. bio
arg. harch
seih scare
Seamorama
0.7558
(1730)
0.6653
0.746
0.270K
0134388
0.7194
0.8190
8.7.5%
0.8121
0.626
0.4392
0.9015
0.2559
0.8926
EVAE 0.7829
0.504
0.6521
0.8169
0.1098
0.5487
0.7463
0.8328
0,7809
SAVE
0.7999
0.5146
0.6579
0.8576
0.2554
0.8615
0.7574
0.8596
0,7983
22

---

Published as a conference paper at ICLR 2026
2.5
CD8T
10015
LAGS
CD14+Mona
5.0
80-
FCGRSAMMono
B
CDAT
1923
12
14
Dendrif
0011
12
NK
R110
canro
HOD
WODK
WODY
FONE
PONE
Figure 14: Violin plots of the top differentially expressed genes (DEGs) predicted by perturbation prediction methods PBMC IFN-3.
23

---

Published as a conference paper at ICLR 2026
Table 19: Comparison of Wasserstein Distance (WD) and Maximum Mean Discrepancy (MMD)
across different cell types and methods (Lower is better: best value bold, second best underlined).
Method
CD14-Mono
FOGR3A
Dendrilic
Average
WD
MMD
WD
MMD
WD
MMD
WD
MMD
WD
MMD
WD
MMD
MMD
WD
MMD
control
4.61
0.07
9.34
0.54
9.09
0..44
4.85
0.10
3.91
0.07
8,06
0.35
5.47
0.10
6.65
0.24
IYAR
4.33
0.25
9.05
0.58
8.73
0..7
5.28
0.41
3.67
0.550
8.43
0.46
5.17
01.30
6.38
0.44
sellstoFacc
1.40
23.76
1.36
13.63
0:47
12:34
0.61
14.00
0.53
CelOT
3.91
0.07
4.54
0.05
9.56
0.54
4.52
0.18
3.49
0.12
6.13
0.13
4.98
0.13
5.30
0.17
SAVE(Our))
4.01
0.11
5,03
0.09
7.01
0.22
4,40
0.17
3.98
0.11
6.35
0.17
5.07
0.09
5.15
0.14
Table 20: Mean Squared Error (MSE) across different cell types (Lower is better: best value in bold, second best underlined).
MSE
CDST
CD14+Mono
FCGR3A+Mono
B
CD4T
Dendritic
NK
mean
control 0.00
0.04
0.03
0.01
0.00
0.02
0.01
0.02
trVAE
0.00
0.03
0.03
0.01
0.00
0.02
0.00
0.01
ScDisInFact
0.20
0.26
0.23
0.16
0.18
0.20
0.17
0.20
ScGEN
0.00
0.01
0.01
0.01
0.00
0.01
0.01
0.01
MFM
0.02
0.04
0.07
0.03
0.03
0.05
0.04
0.04
CellOT
0.00
0.00
0.03
0.00
0.00
0.01
0.00
0.01
SAVE(ours)
0.00
0.00
0.01
0.00
0.00
0.01
0.00
0.00
24


Reviews:
[{"review_id": "IpJk9OU0cN", "reviewer": "Reviewer_ratD", "summary": "The paper proposed a novel generative framework for single cell gene modeling. There are three main ideas: 1. gene block attention to aggregate semantically related genes into blocks and applies a Transformer over these blocks; 2. a latent VAE + Flow Matching module for conditional generation; 3. a condition-masking training strategy. Experiments cover conditional generation (single/dual/multi-condition), batch effect correction (scIB suite), and perturbation prediction (PBMC-IFN), with consistent gains over baselines (scVI, scDiffusion, CFGen, trVAE, etc.).", "questions": "1. How sensitive are results to the source of text embeddings (e.g., different LLMs or just GSEA gene sets) and to the block count L / block size K?\n\n2. What is the runtime/memory profile versus scDiffusion/CFGen at parity?\n\n3. Can you report block-level attention maps and condition-wise shifts (e.g., which blocks drive perturbation responses) to support mechanistic interpretability claims?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Clear modular architecture and formulation presentation.\n\nGene block construction is novel and biologically motivated. \n\nThe proposed method outperforms baseline, which well-supports the claims in the paper.\n\nComprehensive ablation study -- suggesting (a) removing Gene Block Attention degrades WD/MMD and (b) condition masking improves extrapolation for perturbation prediction\n\nImpressive training efficiency by using block attention.\n\nGood reproducibility -- code and hyperparameter settings are publicly available.", "weaknesses": "1. The biological validity of LLM-based semantic grouping from NCBI descriptions is plausible, but risks text-space biases and possible drift from functional co-expression or pathway structure. A comparison against pathway/GRN-based groupings (e.g., MSigDB, Reactome) would strengthen the claim that semantics beats alternatives. \n\n2. WD/MMD at the distribution level and UMAP are helpful but can be insensitive to gene-level calibration.\n\n3. The paper adopts the affine path and CFG-style guidance; however, comparisons to diffusion-style latent generators beyond scDiffusion (e.g., alternative probability paths or ODE solvers) are limited.\n\n4. While baselines are strong and described, more clarity on tuning parity and parameter budgets would improve fairness claims (e.g., scDiffusion vs. SAVE parameter counts/training budgets). \n\n5. The method motivates blocks as biologically meaningful; an analysis that profiles top genes per block, enrichment for known pathways, and how specific conditions modulate block-level attention would amplify the biological insight.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "HKHUBGUApB", "reviewer": "Reviewer_16e8", "summary": "SAVE is a method that uses conditional flow matching on latent embedding to denoise and reconstruct cell data. The gene is first clustered with llm embedding. Similar genes are then grouped together as a gene block. Batch and cell type are used as conditional information for double conditionals and single conditional information such as cell types. The latent is generated from the gene blocks and denoised with flow matching. The final latent is then passed through the decoder to form a reconstructed gene block. The methodology contributions from SAVE are Gene Block Attention where gene embeddings are clustered before passing to a transformer block, and masked conditionals injected to the transformer processing latent information. The model was evaluated on conditional generation, batch effect correction, and perturbation effect prediction with datasets from blood, brain in human and mice.", "questions": "- The link to the code repository [here](https://anonymous.4open.science/r/submit-code-3E75) all showed \"file not found\". Please ensure the code is available for review.\n- For double conditional generation, if the batch information is provided how would out-of-distribution generation be possible for a batch never included before? As well, is this additional batch conditional included in the train/test of other baselines?\n- Do you have results of the perturbation experiments in other forms than correlation metrics (and MSE in the appendix), such as MMD, WD? \n- Why is CD14+Mono perturbation result in Table 16 and Table 5 missing for scGEN? How did it fail under default experimental setup?\n- For the perturbation experiment, can ablations of gene block be done on the results on Table 5? Since the genes are already grouped via the block mechanism, predicting perturbation may become much easier than non-blocked mechanism.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The methodology which combined several ML methods is interesting and some of the results are compelling in double conditional generation. There are several datasets used across different tissues and species, which provides a stronger support for the claim on generalization. The results are carefully separated by categories of cell type for better understanding the strength and weaknesses of the method. The performance was generally strong for all three tasks.", "weaknesses": "The author should provide more quantitative information for the purpose of evaluating the effectiveness of perturbation prediction. The metric used was PCC and $R^2$ (and MSE in the appendix), which are both correlation measures instead of WD and MMD. There are also several other models that predicts perturbation effects, such as [cellOT](https://doi.org/10.1038/s41592-023-01969-x), and [meta flow matching](https://arxiv.org/abs/2408.14608). It is unclear how SAVE compares to the current SOTA on perturbation prediction. \n\nThere are also some formatting issue including missing section hyperlink in the results, as well as unclear labelling of the main diagram. The author should proof read and correct those mistakes.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wYK2MdNLEd", "reviewer": "Reviewer_a9ki", "summary": "The paper proposes a unified generative framework for scRNA-seq that (i) groups genes into semantically defined gene blocks using LLM-derived gene embeddings, (ii) applies a conditional Transformer with Adaptive LayerNorm (AdaLN) to inject multi-factor conditions (batch, cell type, disease, protocol, etc.), and (iii) couples this with flow matching in latent space to enable flexible conditional generation, including unseen condition combinations.", "questions": "The paper adopts affine flow matching in latent space and combines it with classifier-free guidance, which is elegant, but there’s no comparison to latent diffusion or to a simple conditional ODE on top of the VAE to show why Flow Matching was preferred (stability? speed? better extrapolation?).", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper correctly notes that many single-cell generative models treat genes as flat tokens, ignoring biological structure and struggling with combinatorial conditions. SAVE’s gene-block idea is a plausible way to add structure.\n2. Same architecture handles conditional generation, batch integration, and perturbation prediction. That’s attractive for labs that don’t want three separate models.", "weaknesses": "1. Gene-block construction is underspecified for reproduction. The method relies on LLM-derived gene embeddings + optimal-transport clustering to form balanced blocks, but the paper does not fully quantify: what text fields from NCBI were used, which LLM/encoder, how sensitive performance is to mistakes in gene descriptions or to species-specific vocabularies.\n2. SAVE uses a VAE + Transformer over blocks + flow matching + AdaLN. That’s quite a stack. There is a note that all experiments ran on a 3090 with shared hyperparameters, but no training time, memory profile, or comparison to lighter baselines is given. For large atlases (millions of cells), this matters.\n3. Evaluation axes are mostly distributional. WD/MMD and scIB show that the clouds overlap, but users often care about gene-level faithfulness for downstream DE, pathway scores, or ligand–receptor analysis. Only in the perturbation section do we see gene-level metrics (PCC, R²), extending that style of evaluation to the other datasets would strengthen the paper.\n4. The paper claims “broad utility in virtual cell synthesis and biological discovery,” but doesn’t show a biological discovery enabled by SAVE.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wt0yX86jBx", "reviewer": "Reviewer_VUna", "summary": "This paper presents SAVE, a conditional generative framework for single-cell RNA sequencing (scRNA-seq) data based on a variational autoencoder with a Transformer backbone. SAVE introduces a biologically motivated gene-block attention mechanism that aggregates groups of genes into block-level tokens to capture co-regulation and pathway-level structure. Condition-specific effects are incorporated through Adaptive Layer Normalization (AdaLN), while a dual masking strategy on condition labels and latent codes enhances robustness and generalization. The framework is evaluated across three tasks—conditional single-cell generation, batch correction, and perturbation prediction and compared against established baselines including CFGen, scVI, and scDiffusion.\n\nThe paper includes a careful analysis of evaluation metrics (Wasserstein Distance, MMD, PCC, and MSE), extensive ablations on the gene-block design, and discussions of dataset- and model-specific limitations. Overall, SAVE aims to provide a unified, biologically grounded model for multi-condition single-cell data generation.", "questions": "See weaknesses.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Biologically grounded architectural design.\nThe gene-block attention mechanism is an elegant way to encode biological priors into a Transformer framework. By grouping genes into functional or co-expression blocks, the model captures higher-level dependencies that would be difficult to learn from individual gene tokens. The accompanying ablation study (varying block size) provides strong empirical evidence that this inductive bias improves both performance and computational efficiency.\n\n2. Rigorous and transparent evaluation.\nThe experiments are thorough and well-motivated. The authors provide detailed preprocessing pipelines, normalization strategies, and metric definitions, which help ensure reproducibility. \n\n3. Comprehensive comparisons and analyses.\nThe experimental section includes meaningful comparisons to strong baselines, alongside careful discussion of potential confounding factors such as size-factor grouping and normalization space. The analyses convincingly explain discrepancies between quantitative metrics and qualitative observations.\n\n4. Good result interpretability.\nBeyond standard distributional alignment, the study evaluates gene-level fidelity and provides insight into how SAVE captures biologically relevant structures, lending credibility to its claims of biological plausibility.", "weaknesses": "1. Limited evaluation scope on perturbation modeling.\nWhile the paper demonstrates SAVE’s versatility across multiple tasks, the perturbation prediction experiments are limited to a narrow set of baselines. Comparisons to more recent flow-matching or optimal-transport–based approaches would further support claims of generalization in conditional settings.\n\n2. Decoder design justification remains empirical.\nThe use of a fully connected MLP decoder is empirically justified but lacks a stronger probabilistic or biological rationale. While the arguments against negative binomial modeling are sound, exploring hybrid or auxiliary likelihoods could improve interpretability without compromising stability. For example, a flow-based decoder on top of a transformer embedding is a reasonable alternative.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)