Doloris: Dual Conditional Diffusion Implicit Bridges with Sparsity Masking Strategy for Unpaired Single-Cell Perturbation Estimation
Authors: Changxi Chi
Jun Xia
Yufei Huang
Zhuoli Ouyang
Cheng Tan
Yunfan Liu
Jingbo Zhou
Chang Yu
Liangyu Yuan
Siyuan Li
Zelin Zang
Stan Z. Li
Venue: ICLR 2026 Poster (2026)
Keywords: unpair transition
diffusion
Single-Cell Perturbation
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Estimating single-cell responses across various perturbations facilitates the identification of key genes and enhances drug screening, significantly boosting experimental efficiency. However, single-cell sequencing is a destructive process, making it impossible to capture the same cell's phenotype before and after perturbation. Consequently, data collected under perturbed and unperturbed conditions are inherently unpaired, creating a critical yet unresolved problem in single-cell perturbation modeling. Moreover, the high dimensionality and sparsity of single-cell expression make direct modeling prone to focusing on zeros and neglecting meaningful patterns. To address these problems, we propose a new paradigm for single-cell perturbation modeling. Specifically, we leverage dual diffusion models to learn the control and perturbed distributions separately, and implicitly align them through a shared Gaussian latent space, without requiring explicit cell pairing. Furthermore, we introduce a sparsity masking strategy in which the mask model learns to predict zero-expressed genes, allowing the diffusion model to focus on capturing meaningful patterns among expressed genes and thereby preserving diversity in high-dimensional sparse data. We introduce \textbf{Doloris}, a generative framework that defines a new paradigm for modeling unpaired, high-dimensional, and sparse single-cell perturbation data. It leverages dual conditional diffusion models for separate learning of control and perturbed distributions, complemented by a sparsity masking strategy to enhance prediction of zero-valued genes. The results on publicly available datasets show that our model effectively captures the diversity of single-cell perturbations and achieves state-of-the-art performance. To facilitate reproducibility, we include the code in the supplementary materials. Code available at \url{https://github.com/ChangxiChi/Doloris}.

Published as a conference paper at ICLR 2026
DOLORIS: DUAL CONDITIONAL DIFFUSION IMPLICIT BRIDGES WITH SPARSITY MASKING STRATEGY FOR UNPAIRED SINGLE-CELL PERTURBATION ESTIMA- TION
Changxi Chil-2, Jun Xia", Yufei Huang? Zhuoli Ouyang,, Cheng Tan Yunfan Liu?, Jingbo Zhou?, Chang Yu², Liangyu Yuan", Siyuan Li?, Zelin Zang** and Stan Z. Li
1 "Zeejinng University Westlake University
"The Hong Kong University of Science and Technology (Guangzhou)
*Centre for Artificial Intelligence and Robotics Hong Kong Institute of Science & Innovation,
Chinese Academy of Sciences
Southern University of Science and Technology
Shanghai Al Laboratory
"Shanghai Jiao Tong University
(chichane changgn, xiajun, xangzelin) edu.en
ABSTRACT
Estimating single-cell responses across various perturbations facilitates the iden- tification of key genes and enhances drug screening, significantly boosting ex- perimental efficiency. However, single-cell sequencing destructive process, making it impossible to capture the same cell's phenotype before and after pertur- bation. Consequently, data collected under perturbed and unperturbed conditions are inherently unpaired, creating critical yet unresolved problem in single-cell perturbation modeling. Moreover, the high dimensionality and sparsity of single- cell expression make direct modeling prone to focusing zeros and neglecting meaningful patterns. address these problems, we propose a new paradigm for single-cell perturbation modeling. Specifically, we leverage dual diffusion mod- els to learn the control and perturbed distributions separately, and implicitly align them through a shared Gaussian latent space, without requiring explicit cell pair- ing. Furthermore, we introduce a sparsity masking strategy in which the mask model learns to predict zero-expressed genes, allowing the diffusion model to fo- cus on capturing meaningful patterns among expressed genes and thereby preserv- ing diversity in high-dimensional sparse data. We introduce Dolorís, a generative framework that defines a new paradigm for modeling unpaired, high-dimensional, and sparse single-cell perturbation data. leverages dual conditional diffusion models for separate learning of control and perturbed distributions, complemented by a sparsity masking strategy to enhance prediction of zero-valued genes. The results on publicly available datasets show that our model effectively captures the diversity of single-cell perturbations and achieves statc-of-the-art performance. To facilitate reproducibility, we include the code in the supplementary materials. com/ wwtp/Chaang...hh///o......
Code available at attttps:
INTRODUCTION
Different single-cell perturbations, including CRISPR- gene knockouts (Barrangou Doudna 2016 Lino et al., 2018) and small-molecule treatments (Peidli al. 2024). act different layers of celluie fular mechanisms. Despite significant advancements in sequencing technology, producing perturbation data remains costly and time-consuming. As impractical to perform experiments across all cell types and perturbation conditions, accurately predicting perturbation responses under
"Corresponding author.

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Published as a conference paper at ICLR 2026
Other Unperturbed Cell.
RNA-SBq
RNA--Seq
RNA-Seo
ANA-Seq
Perturbation
Perturbation
Unperturbed Cell
Perturbed Cell
Unperturbed Call
Perturbed Cell
Ideal Scenario
b. Realistic Scenario
Figure Single-cell perturbation data are unpaired as cells cannot be measured twice.
novel conditions is crucial. This capability significantly enhances biomedical research, particularly in advancing the understanding of gene functions and accelerating drug screening.
RNA--eq requires cell lysis to release RNA during sequencing, making it an irreversible and destructive process for cells (Mor- tazavi et al. 2008). Consequently, in single-cell perturbation ex- periments, capturing the same cell's phenotype before and af- ter perturbation is not feasible (Fig. [
As a result, single-cell perturbation data are fundamentally unpaired. Although existing methods (Roohani et al.
2022, Hetzel et al.
2022b; Bereket & 2024 Wang et al.)
Karaletsos 2024 Wu et al. 2022 He et al.
2024 Piran et al. 2024] Chi et al. 2025) for predicting cell re- sponses under unseen perturbation conditions have made signifi- cant progress, they often overlook the inherently unpaired nature of single-cell perturbation data, either by forcibly matching sam- ples from the perturbed and unperturbed groups or by disregard- ing their relationships during modeling. On the other hand, while the unpaired nature of the data has been considered in some stud- ies (Bunne et al. 2023 Cao al.) (024), their lack of explicit perturbation modeling limits generalization to unseen perturba- tions. As shown in Fig. 2 directly learning the expression matrix reduces model diversity, as the high dimensionality and sparsity of single-cell data with abundant zero or near-zero values (Xie al.) [2023] Chi et al. 2024) obscures meaningful patterns (Johnstone & Titterington 2009: Bühlmann & Van De Geer 2011).
Figure 2: Intra-distance across different model settings. See
Section 4.5 for details.
To address these issues, we propose Doloris (Dual Conditional Diffusion Implicit Bridges with Sparsity Masking Strategy for Unpaired Single-Cell Perturbation Estimation), new paradigm for modeling single-cell perturbations that predicts cellular responses to unseen genetic and molecular perturbations. Inspired by (Su et al. 2022), Doloris leverages dual conditional diffusion (DDIB) framework to model unpaired single-cell perturbation. To address the challenge of unpaired data, it uses source model for unperturbed cells and target model for perturbed cells, sharing latent Gaussian space to implicitly bridge control and perturbed states, while a perturbation specific em- bedding incorporates gene and molecular perturbation information. Besides, show that adding more genes reduces the SNR (Fig. 8). indicating that higher dimensionality makes pattern learning harder. On top of this high-dimensional background, single-cell expression also sparse (Fig. (5). We introduce a sparsity masking strategy that predicts zero-valued genes and steers the diffusion model focus on expressed signals. Section shows that the sparsity masking strategy is effec- tive in mitigating the model's tendency to overfit zeros and preserving diversity.
The main contributions of our work are as follows:
We introduce Doloris, addresses the challenge of unpaired data by learning separate distributions and perturbed cells while maintaining a shared latent space implicitly bridge control and perturbed distributions, without requiring explicit cell pairing.
paradigm for single-cell perturbation modeling. It explicitly for unperturbed
To handle the sparsity and high dimensionality gene expression, it leverages a sparsity masking strategy that predicts zero-valued genes, ensuring the diffusion model focuses
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meaningful expression patterns instead of abundant zeros. Ablation studies further confirm that the masking strategy effectively mitigates overfitting to zeros and preserving diversity.
We show that Doloris outperforms existing methods across a broad range of evaluation metrics on public genetic and molecular perturbation datasets.
RELATED WORK AND PRELIMINARIES
2.1 PERTURBATION ESTIMATION MODEL
Genetic and molecular perturbations constitute the two main research directions in single-cell per- turbation studies. Existing methods have made significant progress in modeling single-cell perturba- tion responses. Some approaches rely on regression models predict the outcomes of perturbations (Roohani et al.) 2022; Chi et al. 2025) Cheng et al. (025). Other methods employ generative mod- els to reconstruct the distribution of perturbed states (Lottollahi et al. [001 Cui al. 2024 Hetzel
et al. 2022a Wu et al. 2022 Bereket & Karaletsos] 2024, Wang et al.) 2024; Piran et al. 2024).
However, many of these approaches largely overlook the intrinsic relationship between control and perturbed samples during modeling. A separate class of methods enforces explicit pairing between
unperturbed and perturbed samples, which may introduce unrealistic assumptions about the data.
2.2 DIFFUSION PROCESS AND LEARNING OBJECTIVE
In this section, we introduce the basic formulation of diffusion (Lo 2022; Guo al. 2023). Given an input sample Zo, we progressively add noise to it via the forward diffusion process as follows:
Ft vot To + v1 - ãi e, (0,
where t E [0. 1] denotes the time step in the diffusion process, and āg the signal-to-noise ratio at step The objective of the diffusion model co is to predict the true noise from the noisy sample zt- The formula is as follows:
C Ezg ((..).
[lle- (x)
2.3 DDIM INVERSION
The DDIM (oog et al. 2020 proposes straightforward inversion technique based the ODE process, which significantly accelerates the inversion of by back to Tig based on the assumption that the ODE process can reversed in the limit of small steps, which can be written as:
Ft VI axco(
It-1 = / a--1
+ / - ā, - 1p2 ( (x(,, + T7tt
(3)
Vāz
where 7) determines the stochasticity the forward process, and e, is standard Gaussian noise.
2.4 DDIB INFERENCE
Dual Diffusion Implicit Bridges (DDIB.(Su) al., 2022) provide a mechanism to model transitions
between two distributions by learning separate diffusion models (*) and (t) for source and target domains, while connecting them through shared latent space. Specifically, the process begins by adding noise to sample (s()) from the source distribution follow:
r ODESoLve(Z (e)) ODESoLve(Z,, cg. to. t1) = Dio + S co dit (4)
Then, starting from the latent representation (1), the target diffusion model c/00 performs the reverse denoising process generate sample (t)) in the target domain:
(1) ODESclve(z 1.
(5)
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Generic Molecular
Porturbation
Source Conditional Diffusion Model
Target
Diffusion Model
Control Cell
Latent
Treated
Type
ODESolve(x 23 co019),0111 ,011
ODESolve(x com(00 co100,100)
Figure 3: Overview of Doloris. Doloris predicts cellular responses under unseen perturbation ditions. The source model first maps an unperturbed cell x" into the shared latent space by applying a DDIM-based forward process conditioned on covariates con(s), obtaining the latent embedding x!. Conditioned on a given perturbation covariates cou("), the target model then performs DDIM- denoising from x to generate the predicted perturbed cell æ'. For clarity, only the core framework shown here. The mask model will introduced later in detail.
3 METHODOLOGY
In this section, we introduce our proposed model Doloris. The overview is shown in Fig. Specif- ically, the source model learns the distribution of unperturbed cells, while the target model learns the distribution of cells under various perturbation conditions. By using a source model and target model that share a prior space, we align the distributions of unperturbed and perturbed cells, thereby addressing the issue of unpaired data. It is worth noting that Fig. illlustrate only the core frame- work. addition, Doloris employs sparsity masking strategy predict zero-valued genes. The details of the mask model are presented in Sec. 3.5
3.1 INPUT AND OUTPUT
In the single-cell perturbation prediction task, our goal is to predict the gene expression levels of cells under specific perturbation conditions. During training, the model takes real cell samples as input to learn the transition from the true expression distribution to a Gaussian noise distribution (Section 3.3 and Section 3.4p, where the source model conditioned on cov(") and the target model conditioned ft) At the same time, the mask model learns the probabilities of gene acti- vation under perturbation (Section 3.5). which are conditioned solely on (o During inference, control cell sample x and condition (o)(") are input to generate latent embedding z', which is then denoised under the given perturbation condition (") to output the predicted perturbed gene expression. See Section 3.6 for details.
3.2 DATA PREPROCESSING
We first apply the SCANPY package Wolf et al. (2018) perform loglp normalization the gene expression data. Here, N represents the dimensionality of the gene expression vector for each single cell. To facilitate stable training, normalize the gene expression values to the range 00, 1] using the max value Zmer from the training set after splitting the dataset as: x' zmex predictions, we restore the normalized values back to the original scale by multiplying by Emaz-
When generating
3.3 SOURCE MODEL FOR THE DISTRIBUTION OF UNPERTURBED CELLS
The source model is conditional diffusion model designed to capture the gene expression distribu- tions of unperturbed cells. models the alignment control cells under different conditions (here represented by cell type labels) with standard Gaussian latent space.
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Unlike conventional diffusion models (Guo et al. 2023). which predict the noise each time step 2). modeling the noise in gene expression data is particularly challenging due to its complexity and weak structure. Therefore, model directly predicts In, the clean gene expression data. These two parameterizations are theoretically equivalent because (Luo 2022
3t
0g
(6)
Formally, given a control cell sample z6 from cell type et drawn from the unperturbed distribution (a) Pet we obtain the noisy sample 2 by applying forward diffusion process (Eq. 1
Va zú + -i-at āz (0,,1
The model outputs can be uniformly written as:
f = x (xf, coul*)), cool*) = {ct}
(8)
Considering the sparsity of gene expression data, we design mask model, trained independently from the main model, to predict which genes are zero-valued. Consequently, the diffusion model computes the loss only over expressed genes during training. Finally, the diffusion model is trained by minimizing the reconstruction loss between the predicted and true clean gene expression:
M @ (af
Xg (5) (2f t, coo())))
((*)
E too()
(9)
E. Mg
here, M is a binary mask vector defined as:
if o #
M
(10)
0, otherwise
3.4 TARGET MODEL FOR THE DISTRIBUTION OF PERTURBED CELLS
The target model is largely analogous the source model, with the main difference being that learns the distribution of cells under various perturbation conditions, conditioned on both cell type of and perturbation P. Given treated cell sample z from cell type drawn from the perturbed distribution p& we obtain the noisy sample x² at timestep obtained from the perturbed cell a/:
x = Vāi = + VI- c,E (O,
(11)
Considering that perturbations are applied to unperturbed cells to simulate their responses, we need to provide the target model with information about the unperturbed group. However, since the pertur- can't can't directly input sample from the unperturbed group. Furthermore, using only the expectations Pea E R. of unperturbed group gene expression (()) unreasonable, as it disregards cell heterogeneity. During training, random Gaussian noise is added internally to Het with scale σet (Eq. 12) to preserve cellular heterogeneity. Importantly, this does not assume that gene expression follows Gaussian distribution, but rather serves stochastic mechanism to avoid collapsing to mean profiles.
bation data is unpaired,
Enoisy Met det -E, 10,
(12)
Finally, the objective the target model is analogous to the source model, except that it learns from perturbed cells under specific perturbation conditions. Formally, the loss is defined as:
M @ (a) 200 (z), 209(2 cou(()))))
(+))
F (c)
(13)
E, M
where M is binary mask vector defined in Eq. 10 computed based the clean sample znj For notational simplicity, define cov(*) {ct, Met, Tet . P), where et denotes the cell type, Met and
aa represent the expectation and standard deviation of the corresponding unperturbed distribution
p&, and P denotes the perturbation.
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3.5 SPARSITY MASKING STRATEGY FOR ZERO- VALUED GENE PREDICTION
High-dimensional data are inherently challenging, as learning meaningful patterns becomes increas- ingly difficult when the number of features grows (Johnstone & Titterington 2009 Bühlmann & Van De Geer (01TT) In the context of single-cell expression, our analysis shows that as more genes are considered, the relative signal-to-noise ratio (SNR) of the expression data decreases significantly (Fig. (). indicating that pattern learning becomes more difficult in this figh-dimensional space. On top of this high-dimensiona challenge, single-cell expression also sparse (Fig. 5 This sparsity can cause the model to overfit the abundant zeros, obscuring meaningful terns. To address this, we introduce a sparsity masking strategy that predicts silenced genes under perturbation, ensuring that the diffusion model focuses truly expressed genes and learns non- trivial perturbationnsseciifs patterns instead of collapsing to zero sero-dominant solutions.
cntrrrattio--ppccffei pat-
Specifically, besides computing the diffusion loss only over expressed genes during model training (Eq. 9 and Eq. [3,. the sparsity masking strategy also requires an additional Mask Model fgg to be trained. This Mask Model predicts which genes are silenced after each perturbation. The output of fng can be interpreted as probabilities of gene activation, and the final training objective to minimize the enoss-yntropy loss follow:
N
Liaak
Σ
M log(tn((cou()) + (1 - Mt) log(1 - thg (cou("))
(14)
here M is obtained from the observed cell sample zo under perturbation P and cell type el using Eq. 10 However, it only characterizes the predicted marginal distribution. How to derive meaningful samples from this predicted marginal distribution will be discussed in the following section.
3.6 INFERENCE
Inference consists of two main steps. First, we generate continuous gene expression values under perturbation conditions using DDIB inference (Sec. 2.4). Second, the Mask Model predicts the expression states of genes after perturbation. In this section, we provide a detailed explanation of how these steps are implemented.
Conditioned on perturbation P' and cell type ct, we first generate continuous gene expression values using DDIB inference, as illustrated in the lower part of Fig. 3 Specifically, we first randomly sample control cell x" from cell type ct, and then apply forward diffusion process obtain the corresponding latent embedding x¹ using source model x/")
= ODESoll x/ (,)() ..co(())0,01 00
(15)
where (+ {ct]. Then, starting from the latent embedding x', the target model x performs the denoising process to generate the predicted gene expression profile x² under perturbation P. We note that during inference, we assume a true control cell sample xx as the starting point. Therefore, unlike during training. there is no need to construct the input using the mean and standard deviation of the unperturbed group. The actual sample xf is used directly in place of Tnoisy (Eq. 12h.
a ODESolve(r': 20) coo 1,
(16)
where (t) = {ct, 2 PJ.
For gene activation prediction, we first feed the control sample xf with the given condition cov(1) into the Mask Model mmg which outputs probability score Ps. E [0, 1] for each gene being active. However, directly drawing independent Bernuulli samples from these probabilities severe errors and yield globally inconsistent gene activation patterns. To address this, we propose more coherent strategy that first identifies caining-condition subsets with empirical marginal dis- tributions similar to Pa,, and then updates samples from these subsets according to the predicted probabilities to obtain the final binary activation mask M E {0, 1} (Appendix A.11 for details).
accumulate
Finally, the prediction is obtained by applying the sparsity mask M to the predicted continuous gene expression values x' via element-wise multiplication, followed by rescaling to the original scale.
f (M a x²) Fxnax
(17)

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3.7 IMPLEMENTATION
During training, we separately optimize the dual diffusion models (x and & and the Mask Model mg. Since the source and target models share the same architecture, with the target model only requiring additional conditioning inputs (e.g., perturbation P. etc., see Sec. 3.4, we unify them into a single implementation that jointly handles both cou(.) and cov to simplify training.
The embedding of cell type et is directly learned trainable label representation from the training data, without relying on external models. After receiving perturbation information, the model passes it through perturbation--seeific embedding module, which generates conditional signals for gene and molecular perturbations. Specifically, for gene perturbations, we follow the embedding strategy of (Chi et al., 2025). which enables our model to handle multi-gene knockouts and capture combi- natorial perturbation effects. For molecular perturbations, we leverage pre-trained model (Zhou al., 2023) to extract molecular representations, which are then used as conditional inputs for the diffusion model to guide generation.
4 EXPERIMENTS AND RESULTS
4.1 DATASETS
We utilize the Adamson (Adamson et al. 2016) and Norman Norman et al., 2019) datasets for CRISPR knockouts, and the sci-Plex3 (Srivatsan et al.) 2020b) dataset for chemical perturbations.
Detailed preprocessing and data splitting procedures are provided in Appendix A.2
4.2 EXPERIMENT SETTINGS
The model is trained using the A (Loshchlooy 2017) optimizer with a learning rate of 0.001 and batch size of 32. The diffusion process configured with total of 500 steps. For inference, we adopt DDIM (Song et al. (020) sampling with 50 steps. For datasets Adamson, Norman and SciPlex3, training steps are adjusted 10, 000, 10, 000 and 100, 000, respectively. All our method and its competitors are conducted using one Nvidia A100 80G GPU.
4.3 DOLORIS OUTPERFORM EXISTING METHODS
For evaluation, we observe strong heterogeneity in single-cell data, where many differentially expressed (DE) genes exhibit bimodal distributions under the same condition (Fig. 4.. This limitation renders expectation-based metrics unreliable. In particu- lar, for bimodal gene expression distributions, the conditional mean is not biologically meaningful, and metrics such as RMSE computed on the mean fail to capture the true distributional characteristics. To address this, we introduce Energy Distance (E- distance) and Earth Mover's Distance (EMD). E- distance captures overall distributional alignment by considering both inter-group and intra-group dis- tances, while EMD quantifies gene-level shifts by measuring the minimal cost to align predicted and true distributions. Together, they provide a com- prehensive and robust assessment of model perfor-
Unporuraad
Perturbod
2.0
15-
Expressoon
3:0
0.5
0.0
C209
Doma
HERP101
ZWF328
pDra
Hones
SUCMA2
soraL
crapp
TRIUi
Figure 4: Under the same experimental con- dition, many genes show a bimodal distri- bution. The figure shows top DE genes for ZNF326 knockout versus unperturbed cells.
mance at both the population and gene levels. Detailed computation procedures are provided in the Appendix A.6
Table I shows that Doloris outperforms GEARS (Roohani et al. 2022 graph VCI (Wu al. 2022
scGPT (Cui et al.) 2024), BioLord (Piran et al. 2024). and GRAPE (Chi et al. (025) across most evaluation metrics, all of which rely on forced pairing of perturbed and unperturbed cells during training. For the regression models, this setup tends to bias learning toward the mean of the data, preventing the capture of the heterogeneity of single-cell gene expression profiles. Methods such as
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Table 1: Comparisons on Adamson and sci-Plex3 datasets. Metries include RMSE, E-distance, and EMD computed on all and top-20/40 DE genes. Tasks correspond to unseen single-gene and drug-ced cell lina-d perturbations, respectively.
Model
DE20
RMSELJ
B-distancet()
EMD(J)
RMSEL)
Eddistano(()
EMD())
RMSE())
E-distanco(() EMDX))
Unseen single genetic perturbation prediction resulls
Doloris
=0,0103
0.0336
0.4682
-0.8
+0.0033
0.0348
+0.0506
0,1094
+0.1930
0.4653
000514
0,0789
+0.0578
0.0987
0.4976
1847
+0,0452
0,0811
ambda
0,0805
1,9939
0.0906
0.2539
0.6996
0.0914
0.2197
0.7229
0.0950
=0.0257
12.1
10,040
+0.0192
+0.2997
200076
+0,089
#0.2615
+0.0389
045510
0.8705
0.0444
0.1850
0.7514
0.1528
0,1697
0.7648
0.1503
GRAPE
=0,0100
10.084
10.0024
10.0066
10,0523
20,0344
10,0047
10.0565
10.0182
0,8921
0.1298
0.7935
GEARS
=0.0088
13.1304
+0.0027
+0.0078
+0.1245
00.0324
+0.0054
#0.1273
+0.0231
xcGPT
=0.1482
0.5372
2.6318
0.1724
+0.1346
0.7151
1
00,00
0.3895
220
0,7021
1.4444
+0,0866
0.3781
linear
0.0473
088688
0.3733
0.2143
0,853
0.1702
2007
0.8958
0.1631
20,0008
10.0251
10.0024
10.0068
10.0525
100022
10,000
10.0429
10.0199
Unseen molecular perturbation prediction results
Doloris
-0.0157
0.0287
1092190
0.4055
10.0051
0.0265
10.0112
0,0625
10.1710
0.2484
200026
0.0743
10.0600
0.0547
10.1671
0.2406
10.0219
0,0649
BioLoed
=0.0180
0.0409
1947
1,2739
+00003
0.7733
+0,0622
0,1094
+0.1529
08882
+0.064
0,2157
+0,0497
+0.1451
1,0314
+000477
0.1920
CPAmCPA
0.0570
0.7847
0.0838
0,1462
0,4717
0.1836
0.1314
0,5008
0.1784
=0.0130
10.1029
+0,071
+0.1571
200358
100167
10,1659
CPA
=0.0253
0.0697
10.1336
0.9894
10.0161
0.1357
10.0935
0,2006
10.9768
0.7377
2006667
0.3761
10.0667
0.1
11,890
1/07994
10.0357
0.3856
GraphVCI
=0.0772
0.6212
+0.1823
0,8393
0.0986
0,5856
+0.1275
0,4958
+0,0379
0.2016
+0.1231
0.6007
+0.1347
0.5174
+0.0288
0.1861
HSD17812
HSD17812 0.06
A549, Enzastaurin 1PM
(d). A548 Enzastaurin 1pM 0.05
PCC-09678
POC-00.500 5050
POC-0.5600
PCC-09514
0.0
68
0.3
6.4
02
6.2
00
8.6
0.5
0.4 1.5
02
3.8
0.0
0.4 0.6
3.2
Prediction
Prediction
Prediction
Figure 5: Visualization of predicted gene activation probabilities by the Mask Model. Panels (a) and (c) show the results under perturbation of HSD17B12 and 1349stnzzttaurin- IyM (cell type- dougedosage), respectively, while panels (b) and (d) display only genes with predicted activation probabilities greater than 0.05 from (a) and (c).
CPA (Lotfollahi et a..), chemCPA (Hetzel et al. 2022a) and sclambda (Wang et al. 2024) further underperform because some of them reconstruct only perturbed cells without explicitly modeling the transition from the unperturbed state. Notably, while linear baseline (Ahlmann- Eltze et al. (025) achieves competitive performance against some deep learning models, it fundamentally lacks the ca- pacity to model complex. non-linear distributional shifts. More importantly, the modeling paradigm employed by Doloris overcomes the challenges posed by high-dimensional and sparse single-cell data. By leveraging an additional sparsity masking strategy, the diffusion model can focus on ex- pressed genes rather than fitting zero-valued entries, thereby capturing more biologically relevant information (Fig. 2). Crucially, Doloris addresses the limitations of paired data by employing dual implicit bridges, which explicitly and flexibly model the relationship between unperturbed and per- turbed states.
To validate the effectiveness of the Mask Model, Fig. showw that it achieves good performance in predicting gene activation probabilities under different perturbation conditions. We compared the predicted gene activation probabilities for all genes with the empirical probabilities for genes with expression levels greater than 0.05.
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4.4 DOLORIS PERFORMS WELL ON OOD DRUG AND DOUBLE GENE PERTURBATION
To further validate the effectiveness of Doloris, we evaluate its performance on double gene knock- outs using the Norman dataset (Norman et al. 2019) and on out-of-distribution (OOD) drugs (de- scribed in Sec. 4.1 in Tab. 2 Double gene knockouts involve complex vene-gene interactions, and experimental results show that our model effectively captures these interactions. To predict the effects of double gene perturbations, we use all observed samples under single gene perturbations and unperturbed conditions as the training set. It has been previously demonstrated that OOD drugs (Srivatsan et al. 2020a; Hetzel et al.) 2022a), which were not observed during training, predomi- nantly target epigenetic regulation, tyrosine kinase signaling, and cell cycle regulation. These drugs representative of key biological processes and are often distinct from the drug in the training set. Our model demonstrates superior performance, suggesting that it better captures the effects of unseen molecules on cellular behavior. Importantly, our design allows to infer the effects of previously unseen drug molecules as well as unobserved gene perturbations.
Table 2: Evaluation of model performance on dou- ble gene (Norman) and OOD drug perturbations (sci- Plex3). We highlights the top two methods in red and orange, respectiell.
Adammonn
Sci Sci-Plexd
0.75
0.70
0.25
0.45
0.40
0.60
0.55
0.30
Durille youe pettorfutions
0.50
Dakerts
LOKPS:
GEARS
0.45
DE20
D640
0.20
DE20
D640
RMSR 1650
8.3631 400034
D 13555
010
0.3631
39995
-004132
+30097
RMSR D610
F.dkozane All
84819 -0.1753
8.2M05 -0:977
02133
1611
0.765
0.7617
441 6410616
0.7784
-0 09755
+38977
+0.1043
0.09
0.08
0.08
0.07
8.8143
10.1534
08835
(165
019601
10/613
0.561
-0 000666
+319937
FMID All
8.0779
100933
0.000
000380 100001
81000
-0
+31911
0.07
0.05
EXT
8.2025
100815
02175
10:04
100008
01000
+211190
0.00
0.05
perter bedien
0.55
3.04
Daledt
G=gavCC
0.04
RMSE DE20
RMSE All
8.547
8.154 20.1133
#00335
0,5600
0.2002
200800
50,01.0
0.543) 2AL0852
0.3351 a0 1665
12/142
401333
0.23
0.02
RMSE
#00900
401175
Dolors
wio No.
who Istere
weo Mask Strttgyy
Exdotans DE20
8.4744 =5 -5.197
0.337 00 22-2
0.7123 on 1945
102279
E-Jatanse D640
0.839
-0.1643
0.710
02 2014
03445 =41 1914
+02571
=00038
DE20
133455
+31855
Figure 6: Ablation study results.
EMD DE40
8.1071 300014
0.3004 =0.0043
0,2176
on 2500
101705
4.5 ABLATION STUDY
To further evaluate the effectiveness of Doloris, we compare with the following methods through an ablation study. 1)w/o Me. de: Excludes the mean and variance of the unperturbed group from the
model input. 2)w/o latent: During sampling, the input latent embedding z' in Eq. 16 b replaced with random Gaussian noise. 3)w/o mask model: Removing the mask model forces the model to predict the expression of all genes during training. The results are shown in Fig
The experimental results indicate that the Pe, Ge of unperturbed cells are crucial, as perturbations essentially represent a transition from the unperturbed state. Compared to random Gaussian noise, latent embeddings generated by adding noise to unperturbed cells provide a more structured and interpretable initialization, leading to significantly improved generation quality and modeling effi- ciency. Experimental results highlight the critical role of the mask model. Due to the sparsity of gene expression data, with many zero-valued genes, models without masking tend to focus on pre- dicting zeros, which diverts attention from actively expressed genes and reduces both diversity and biological fidelity in the generated profiles. As shown in Fig. [ the intra-class distances (Eq. 20) of predictions decrease in models trained without masking strategy.
u
CONCLUSION
In this work, we present Doloris, a novel paradigm for single-cell perturbation modeling that explic- itly addresses the challenges of unpaired data. By leveraging dual conditional diffusion framework, our approach aligns the distributions of unperturbed and perturbed cells without requiring explicit sample pairing, while a perturbation-speciff embedding module provides genetic and molecular level conditional signals. To handle the sparsity and high dimensionality of single-cell gene expres- sion, introduce mask model that predicts zero-valued genes, ensuring that the model focuses
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on biologically meaningful signals and preserves diversity. Furthermore, we propose biologically grounded evaluation metric that captures cellular heterogeneity and the diversity of single-cell re- sponses. Experimental results genetic and molecular perturbation datasets demonstrate that Do- loris outperforms existing methods and generalizes to unseen perturbations. Our work establishes a new modeling paradigm for single-cell perturbation, enabling more accurate and biologically faith- ful predictions of cellular responses under novel conditions.
ACKNOWLEDGMENTS
This work was supported by National Science and Technology Major Project (No. 2022ZD01 15101), National Natural Science Foundation of China Project (No. 623B2086), Na- tional Natural Science Foundation of China Project (No. U21A20427), Project (No. WU2022A009) from the Center of Synthetic Biology and Integrated Bioengincering of Westlake University, and the Zhejiang Province Selected Funding for Postdoctoral Research Projects (ZJ2025113).
REFERENCES
Britt Adamson, Thomas M Norman, Marco Jost, Min Y Cho, James K Nuñez, Yuwen Chen, Jacque- line Villalta, Luke A Gilbert, Max Horlbeck, Marco Hein, et al. A multiplexed single-cell crispr screening platform enables systematic dissection of the unfolded protein response. Cell, 167(7):167-1182, 2016.
Constantin Ahlmann- Eltzznn-Ellze, Wolfgang Huber, and Simon Anders. Deep-learning-uee basend gene pertur- bation effect prediction does not yet outperform simple linear baselines. Nature Methods, 22(8): 1657-1661, 2025.
Rodolphe Barrangou and Jennifer A Doudna. Applications of crispr technologies in research and beyond. Nature biotechnology. 34(9):933-941, 2016.
Michael Bereket and Theofanis Karaletsos. Modelling cellular perturbations with the sparse additive mechanism shift variational autoencoder. Advances in Neural Information Processing Systems, 36, 2024.
Peter Bühlmann and Sara Van De Geer. Statistics for high-dimeensional data: methods, theory and applications. Springer Science Business Media, 2011.
Charlotte Bunne, Stefan G Stark, Gabriele Gut, Jacobo Sarabia Del Castillo, Mitch Levesque, Kjong- Van Lehmann, Lucas Pelkmans, Andreas Krause, and Gunnar Rätsch. Learning single- cell perturbation responses using neural optimal transport. Nature methods, 20(11):1759-1768 2023.
Yichuan Cao, Xiamiao Zhao, Songming Tang, Qun Jiang, Sijie Li, Siyu Li, and Shengquan Chen. scbutterfly: versatile single-cell cross-modality translation method via dual-aligned variational autoencoders. Nature Communications, 15(1):2973, 2024.
Jiabei Cheng, Changxi Chi, Jingbo Zhou, Hongyi Xin, and Jun Xia. Prescribe: Predicting single-cell responses with bayesian estimation. arXiv preprint arXiv:2510.07964 2025.
Changxi Chi, Hang Shi, Qi Zhu, Daoqiang Zhang, and Wei Shao. Spatially resolved gene expression prediction from histology via multi-view graph contrastive learning with boitebottle regular- ization. arXiv preprint arXiv:2406. 12229, 2024.
Changxi Chi, Jun Xia, Jingbo Zhou, Jiabei Cheng, Chang Yu, and Stan Z Li. Grape: Heterogeneous graph representation learning for genetic perturbation with coding and non-coding biotype. arXiv preprint wrXiv:2505.03888 2025.
Kwangbom Choi, Yang Chen, Daniel A Skelly, and Gary A Churchill. Bayesian model selection reveals biological origins of zero inflation single-cell transcriptomics. Genome biology, 21(1): 183, 2020.
10

---

Published as a conference paper at ICLR 2026
Haotian Cui, Chloe Wang, Hassaan Maan, Kuan Pang, Fengning Luo, Nan Duan, and Bo Wang- scgpt: toward building a foundation model for single-cell multi-omics using generative ai. Nature Methods, 21(8):1400-1480 1480, 2024.
Mingze Dong, Bao Wang, Jessica Wei, Antonio H de O. Fonseca, Curtis Perry, Alexander Frey, Feriel Ouerghi, Ellen F Foxman, Jeffrey Ishizuka, Rahul M Dhodapkar, et al. Causal identifi- cation of single-cell experimental perturbation effects with cinema-ot. Nature methods, 10(1)): 1769-1779, 2023.
Yuwei Guo, Ceyuan Yang, Anyi Rao, Zhengyang Liang, Yaohui Wang, Yu Qiao, Maneesh Agrawala, Dahua Lin, and Bo Dai. Animatediff: Animate your personalized text-to-image diffu- sion models without specific tuning. arXiv preprint arXiv:2307.04725, 2023.
Siyu He, Yuefei Zhu, Daniel Naveed Tavakol, Haotian Ye, Yeh-Hsing Lao, Zixian Zhu, Cong Xu, Sharadha Chauhan, Guy Garty, Raju Tomer, et al. Squidiff: Predicting cellular development and responses to perturbations using diffusion model. bioRxiv, pp. 2024-12 11, 2024.
Leon Hetzel, Simon Boehm, Niki Kilbertus, Stephan Günnemann, Fabian Theis, et al. Predicting cellular responses novel drug perturbations single-cell resolution. Advances in Neural Information Processing Systems, 35:26711 2022a.
Leon Hetzel, Simon Bochm, Niki Kilbertus, Stephan Günnemann, Fabian Theis, et al. Predicting cellular responses to novel drug perturbations at a single-cell resolution. Advances in Neural Information Processing Systems,
2022b.
Ruochen Jiang, Tianyi Sun, Dongyuan Song, and Jingyi Jessica Li. Statistics or biology: the zero- inflation controversy about scrna-seq data. Genome biology. 23(1):31, 2022.
lain M Johnstone and D Michael Titterington. Statistical challenges of high-dimensional data, 2009.
Christopher A Lino, Jason C Harper, James P Carney, and Jerilyn A Timlin. Delivering crispr: a review of the challenges and approaches. Drug delivery, 25(1):1234-125,, 2018
I Loshchilov. Decoupled weight decay regularization. arXiv preprinl arXiv: 2017.
M Lotfollahi, AK Susmelj, and C De Donno. Learning interpretable cellular responses complex perturbations in high-throughput screens. biorxiv. 2021. 2021.04. 14.439903.
Mohammad Lotfollahi, Alexander Wolf, and Fabian J Theis. segen predicts single-cell perturba-
tion responses. Nature methods, 16(8):715-721, 2019.. 2019.
Calvin Luo. Understanding diffusion models: A unified perspective. arXiv preprint 1rXiv:2208.11970, 2022.
Ali Mortazavi, Brian A Williams, Kenneth McCue, Lorian Schaeffer, and Barbara Wold. Mapping and quantifying mammalian transeriptomes by rna-seq. Nature methods, 5(7): 2008.
Thomas M Norman, Max A Horlbeck, Joseph Replogle, Alex Ge, Albert Xu, Marco Jost, Luke A Gilbert, and Jonathan S Weissman. Exploring genetic interaction manifolds constructed from rich single-cell phenotypes. Science, 365(6455):786-79, 2019.
Stefan Peidli, Tessa Green, Ciyue Shen, Torsten Gross, Joseph Min, Samuele Garda, Bo Yuan, Linus Schumacher, Jake P Kailor-King, Debora S Marks, et al. scperturb: harmonized single- cell perturbation data. Nature Methods, 21(3):531-540, 2024.
Zoe Piran, Niv Cohen, Yedid Hoshen, and Mor Nitzan. Disentanglement single-cell data with biolord. Nature Biotechnology, 11111):678816888 2024.
Qiu. Embracing the dropouts in single-cell ma-seq analysis. nat commun 11: 1169, 2020.
Yusuf Roohani, Kexin Huang, and Jure Leskovec. Gears: Predicting transcriptional outcomes of novel multi-gene perturbations. BioRxiv, pp. 2022-07, 2022.
Jiaming Song. Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502 2020.
11

---

Published as a conference paper at ICLR 2026
Sanjay R Srivatsan, José L CcFFalineFFiueene Vijay Ramani, Lauren Saunders, Junyue Cao, Jonathan Packer, Hannah A Pliner, Dana Jackson, Riza M Daza, Lena Christiansen, et al. Mas- sively multiplex chemical transcriptomics at single-cell resolution. Science, 367(6473):45-51, 2020a.
Sanjay R Srivatsan, José L McFaline-Figuerro, Vijay Ramani, Lauren Saunders, Junyue Cao, Jonathan Packer, Hannah A Pliner. Dana Jackson, Riza M Daza, Lena Christiansen, al. Mas- sively multiplex chemical transcriptomics at single-cell resolution. Science, 367(6473):45-51, 2020b.
Xuan Su, Jiaming Song, Chenlin Meng, and Stefano Ermon. Dual diffusion implicit bridges for image-to-image translation. arXiv preprint arXhv:2203.08382 2022.
Gefei Wang, Tianyu Liu, Jia Zhao, Youshu Cheng, and Hongyu Zhao. Modeling and predicting single-cell multi-gene perturbation responses with sclambda. bioRxiv, 2024.
F Alexander Wolf, Philipp Angerer, and Fabian Theis. Scanpy: large-scale single-cell gene ex- pression data analysis. Genome biology, 19:1-5, 2018.
Yulun Wu, Robert A Barton, Zichen Wang, Vassilis N loannidis, Carlo De Donno, Layne C Price, Luis F Voloch, and George Karypis. Predicting cellular responses with variational causal infer- ence and refined relational information. arXiv preprint arXiv:2210.00116 101112200.0016,,, 2022.
Ronald Xie, Kuan Pang, Sai Chung, Catia Perciani, Sonya MacParland, Bo Wang, and Gary Bader. Spatially resolved gene expression prediction from histology images via bi-modal contrastive learning, Advances in Neural Information Processing Systems, 36:70626-70637, 2023.
Gengmo Zhou, Zhifeng Gao, Qiankun Ding, Hang Zheng, Hongteng Xu, Zhewei Wei, Linfeng Zhang, and Guolin Ke. Uni-mol: A universal 3d molecular representation learning framework. 2023.
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A APPENDIX
A.1
USE OF LLM
The LLM only assisted us in checking spelling and grammar.
A.2 DATASETS DETAILS
This dataset contains 87 types of single-gene perturbations in a single cell type. We perform single-gene perturbation prediction this dataset. For data splitting, 30% of the perturba- tion conditions are randomly selected as the test set, while the remaining perturbations and control cells are used for training. Data preprocessing follows the procedures described in (Chi al. 2025).
Adamson
Norman
This dataset includes both single-gene and double-gene perturbations. In our study, we focus on predicting double-gene perturbations. For data splitting, all control cells and single-gene perturbations are used as the training set, while all double-gene perturbations are reserved for the test set. Data preprocessing follows the procedures described in (Chi et al. 2025)
sci-Plex3 We use to evaluate model performance on out-of-distribution (OOD) drugs and on unseen combinations of cell type, drug, and dosage. The dataset comprises experiments on three cell lines treated with 188 drugs, each at four dosages. For data splitting, we first designate all samples under certain drug conditions analyses reported in Srivatsan et al. (020a);; Hetzel et al. (2022a). For the remaining data, all control group cells are included in the training set. Then, for each experimental condition defined by unique combination of drug, dosage, and cell type, the corresponding group of cells is assigned to the test set with a 30% probability, and to the training set otherwise. Data preprocessing follows the procedures described in (Hetzel et al. 2022a).
the OOD COut-of-Distributt
test set, based on prior
A.3 EFFECT OF THE NUMBER OF FUNCTION EVALUATIONS (NFE)
In addition, we evaluated the effect of the Number of Function Evaluations (NFE) of diffusion sampling steps reconstruction performance. As shown in Fig. 7 using single step results in drastically worse reconstruction metrics, highlighting that multi-step denoising is essential. Increas- ing the number of steps to 30 yields substantial improvements, while further increasing 50 or 70 steps provides only marginal gains. Thus we adopt 50 steps to balance reconstruction quality and computational efficiency.
2:08
0.36
DE20
0.10
0.08
Edistance
0.55
EMD
0.06
0.53
0.05
0.51
0.04
0002
0.49
30
50
70
30
50
70
NFE
NFE
Figure 7: Performance across different NFE.
A.4 COMPUTATIONAL COST
Assuming that the forward and reverse diffusion processes each incur computational cost of N (corresponding to the number of DDIM sampling steps) and that the Mask Model introduces lightweight cost of the theoretical cost per generated sample is 2N
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In the context of large-scale perturbation generation, where there is single control cell type and & distinct perturbation conditions with n samples per condition, we can significantly reduce compu- tation by reusing the latent representations obtained from the forward diffusion process rather than regenerating them for each sample. Letting m denote the number control cells used in the forward m- N.
process, the total computational cost is then given by (1 + N)
For moderate m and large k, this cost is comparable to that of a standard diffusion model which directly denoises n samples, N k n. This indicates that when generating large number of samples, our method has a computational cost similar to standard diffusion.
A.5 CURSE OF DIMENSION
In this experiment, we select the top 50, 100, 200, 500, 1000 and 2000 highly variable genes (HVGs) and compute the signal-to-none ratio (SNR) for each perturbation type using only these genes. To better highlight the relative differences across gene sets, the SNR values are normalized relative to the top 50 genes.
SNR is defined as the ratio of the between-condition variance to the within-condition variance:
SNR c== Mr Moverall
(18)
N Ei=
[ - My. 11
where is the number of perturbation conditions, N is the total number of cells, is the mean expression vector for condition Moverall is the overall mean across all cells, Iy the expression vector of cell i, y4 is its condition label, and e is small constant to prevent division by zero.
The Relative SNR defined
SNR
Relative SNR
(19)
SNR
A.6 EVALUATION METRIC
In this section, we introduce two metrics-Energy Distance (E-distance) and Earth Mover's Dis- tance wEich propose better quantify the prediction performance of single-cell per- turbation models. Given the prediction X = X1, X2..... Xn E T and the true samples Y Y2,,..... Ym E RmxN where n and m denote the number of cells and D the number of genes.
The E-Distance between X and Y defined as:
Dz(X,Y)= = nm
|x - 1
ΣX
ΣΣ
V - Y,l12
m
1=1=1
=1
2 X inter-class distance
intra class distance (X)
intra class distance (Y)
(20)
where || denotes the Euclidean norm.
Different from the traditional formulation of Earth Mover's Distance (EMD) based on optimal trans- port, adopt practical implementation that averages the one-dimensional Wasserstein distances across gene dimensions. Specifically, the EMD between X and Y is calculated as:
DEMD(X, 1 N
Σ JEN
EMD(X.,, Y.,),,
(21)
where X., E TD and Y.₁ Rm denote the predicted and true expression values of gene across all cells, respectively. Each EMD(X..g Y.gg) is computed as the 1D Wasserstein distance between the marginal distributions of gene g.
In summary, our evaluation framework integrates E-distance for population-level structure and EMD for individual gene-level accuracy, ensuring robust and comprehensive assessment.
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1.0
Adamson
Norman
sci-Plex3
Relative SNR
0.8
0.6
0.4
0.2
0.0
top50
top100
top200
top500
topl000
top2000
Figure 8: Trend of Relative SNR as more genes are included. Details of the calculation are provided
in the Appendix A.5
A.7 PERTURBATION MODELING
To model cellular perturbations, we leverage prior biological knowledge in the form of a gene reg- ulatory network (GRN) G E {0, 1JNNN, which is represented unweighted graph capturing relationships among genes. Within our model, Graph Attention Network (GAT) is applied to the GRN generate gene embedding, which acts the perturbation representationfor downstream prediction.
f = GAT(G)
(22)
We chose GAT because its attention mechanism allows adaptive weighting of gene-gena interac- tions, which is particularly useful for modeling regulatory effects under perturbations. To con- struct the initial node features, we aggregated the gene expression data from the training Con- sidering the computational intractability of using individual cell samples directly, we computed the expectation of gene expression for all samples within each perturbation condition. The initial node feature matrix (E R RN*K) was then formed by concatenating these cundition-specinn expecta- tions (E R Np)) ), followed by Principal Component Analysis (PCA) dimensionality reduction Ahhmannn-Hlee et al.) (025). These initialized features serve as static priors and remain frozen tron-trainable) throughout the entire training process.
Unlike random initialization, which treats genes as indistinguishable entities lacking semantic con- text, our data-driven initialization explicitly incorporates the intrinsic biological properties and ex- pression patterns of each gene. This ensures that the model starts with biologically meaningful representation space, rather than learning from scratch.
For gene perturbations, first perform GAT message passing to aggregate regulatory information across the graph. Subsequently, we extract the updated node embedding of the specific perturbed gene from the aggregated graph representations. This context-awaid embedding is then utilized as the perturbation condition. For molecular perturbations, we first extract molecular embeddings using a pretrained molecule model (Zhou al. 2023). These embeddings are then combined with associated treatment information, such as dosage, to form a condition-specific perturbation vector.
A.8 RELATION WITH HURDLE MODELS
Our sparsity masking strategy can be interpreted Hurdle Model applied the single-cell level: the first component models the probability of gene activation, and the second models the expression values for active genes, while explicitly preserving global dependencies across genes.
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A.9 ZERO EXPRESSION CARRY BIOLOGICAL MEANING IN SCRNA-SER DATA
Numerous studies have shown that dropout is not purely random, and many observed zeros carry meaningful biological informatiorCCoi et al. (2020); Qiu (2020); Jiang et al. (2022). Therefore, leveraging gene-gene dependencies to predict gene activation states is fully justified in this setting and does not constitute "big claim".
A.10 OTHER RELATED WORK
Although (Bunne et al. 2023 Dong et al. 2023) also address unpaired data, their task assumes access to both pre- and post post-perturbation cells and focuses on finding optimal pairings between them. In contrast, our task is to predict the pest-perturbation state directly from the control cells and the perturbation condition, which is fundamentally different.
A.11 MASK MODEL PREDICTION STRATEGY
Let the model predict gene activation probabilities from fyg for cell Pão (21.P2..... ........ ,NN). A naive independent Bernoulli sampling would give:
M, Bernoull(yss), i= N,
(23)
which often leads to globally inconsistent masks. To address this, purpose solution as follow.
For given perturbation condition, we first identify a reference subset training cells
Scond E Deond
(24)
here, D denotes the entire training dataset containing all cells under various perturbation conditions. Deand C 'D represents all observed cells under a specific perturbation condition. Scond denotes a sample from D
The empirical marginal activation distributions of cells in the reference subset {g Jiml are quired to be as close as possible to the model-predicter probabilities Ps., Formally. the reference subset Scond is selected from all cells under the same perturbation condition Doond by minimizing the Euclidean (L2) distance between the predicted probabilities and the empirical marginal distributions:
Scoma = arg min DDnnd
ph. - {4e }
(25)
From the selected reference subset Sondd randomly sample real sample:
UniformSample
Scond))
(26)
and then we obtain real mask sample in by applying Eq. 10 8.
We then update the sampled mask mn according to the predicted probabilities pa, using high and low thresholds 5₁ and &, which set to 0.95 and 0.05, respectively:
if Pho 2 5n.
M,
if Pho S ōt, m otherwise,
0,
(27)
Finally, the coherent binary mask for the cell is
M (M, Ma,... ... Mn) (0, 1..
(28)
16


Reviews:
[{"review_id": "peW4np1NXd", "reviewer": "Reviewer_r3Gg", "summary": "The authors tackle the problem of estimating single-cell gene expression under genetic or molecular perturbations, where data is inherently unpaired due to the destructive nature of sequencing. They introduce Doloris, which uses two conditional diffusion models: a \"source\" model for unperturbed (control) cells and a \"target\" model for perturbed cells, implicitly aligned via a shared Gaussian latent space using Dual Diffusion Implicit Bridges (DDIB). To handle sparsity (abundant zeros in expression data), they add a mask model that predicts silent genes, allowing the diffusion process to focus on expressed patterns. During inference, continuous expressions are generated via DDIB, then masked and rescaled. The framework conditions on cell types and perturbations.", "questions": "1. In Fig. 2, why those specific genes (AARS, CARS, etc.)? Are they representative, or cherry-picked? Extend to full dataset stats?\n2. How robust is the model to perturbation types? For example, does it handle dosage dependent molecular perturbations, or only binary knockouts?\n3. Do you have any downstream validation? Beyond metrics, does it recover known biology, like perturbed pathways in KEGG?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "Single-cell perturbation modeling is difficult because scRNA-seq is destructive. We can’t see “before and after” for the same cell. Data is unpaired and high-dimensional + sparse. Existing models often (i) implicitly force pairing or (ii) ignore the unpaired nature, or (iii) regress to the mean and miss heterogeneity. Doloris learns a source conditional diffusion model for control cells and a target conditional diffusion model for perturbed cells, make them share a latent Gaussian space via ODE mapping, so a real control cell is diffused to latent, then denoised to the perturbed state under a specified perturbation. Additionally, they introduce a mask model that predicts which genes should be silent for a given perturbation and cell-type condition. Losses for diffusion are computed only on expressed genes.", "weaknesses": "1. The abstract boasts SOTA on public datasets, but misses comparison against recent unpaired optimal transport methods like scOT, diffusion-based OT or flow matching based OT. \n2. The shared latent space assumes control and perturbed distributions are bridgeable via Gaussian priors, but how is this validated? In Sec. 3.4, adding noise to unperturbed means to preserve heterogeneity is ad-hoc. Why Gaussian, and what's the sensitivity to σ_ct? If perturbations drastically shift distributions, this might fail.\n3. While the method predicts realistic expression distributions, the paper doesn’t show many biological case studies. For example, does the model recover known pathway-level responses?", "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": "eTRGmXFUNv", "reviewer": "Reviewer_NHyz", "summary": "The paper introduces Doloris, a novel generative framework for predicting the gene expression of single cells after a perturbation. The paper addresses two main challenges: (1) the data is unpaired, as one cannot measure the same cell before and after perturbation, and (2) gene expression data is extremely sparse. Doloris addresses the unpaired problem by training two separate diffusion models and aligning them through a shared latent space (without explicit pairing). To handle sparsity, the paper proposes a two-part model, namely a mask model that predicts a binary mask of which genes will be silent, and a diffusion model trained only on the active (non-zero) genes.", "questions": "What is the specific architecture of the diffusion models?\n\nWhat is the specific architecture of the mask model? Is it also conditioned by the GAT embedding?\n\nI think the paper proposes a complex sampling strategy for the binary mask to ensure global consistency. How does this compare to simply thresholding the mask model's probabilities at 0.5? What was the performance gain from this more complex method?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The dual-bridge framework is a novel and effective solution to the fundamental unpaired data problem.\n\nThe paper's emphasis on using distributional metrics (E-distance, EMD) over simple RMSE is well-argued, as these metrics are better suited to capturing the cellular heterogeneity inherent in single-cell data.", "weaknesses": "A significant weakness is the lack of details for the core diffusion models. The paper does not state what neural network architecture is used as the backbone.\n\nThe authors state they use a GAT to embed perturbation information. However, this choice seems arbitrary. The paper provides no ablation studies or comparisons to other GNN architectures.\n\nThe paper fails to connect its sparsity masking strategy to existing, well-established statistical frameworks. This two-part architecture with one model for the zero/non-zero binary outcome and a second model for the non-zero continuous values, is a direct implementation of a Hurdle Model. Drawing this parallel would have strengthened the paper by grounding its components in classical statistical theory.", "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": "cNl8jsGsRS", "reviewer": "Reviewer_hoSz", "summary": "This author with this paper introduces DOLORIS, a new generative framework for predicting the gene expression of single cells after perturbation. The work is well-motivated by the unique challenges of single-cell data: it is unpaired, high-dimensional, and sparse. The proposed solution combines a dual diffusion bridge model with a dedicated sparsity masking mechanism.", "questions": "Beside weakness, I think would be beneficial if authors could briefly answer to some additional questions.\n\n***Regarding the Sparsity Mask:*** Could you elaborate on the potential failure modes of the mask model and how they might impact the final predictions? For instance, if the mask model incorrectly predicts a biologically crucial gene as \"silent\" (inactive), does your framework have any mechanism to recover, or is that information irrecoverably lost?\n\n***Regarding the DDIB Framework:*** Could you provide more intuition on why the shared latent space is sufficient to learn a biologically meaningful transformation? How does the model ensure that a control cell is mapped to a corresponding perturbed cell, rather than just an arbitrary cell from the perturbed distribution that matches the conditioning information?\n\n***Regarding Computational Cost:*** Your model involves two diffusion models plus a mask model. Could you comment on the computational resources required and the inference time per sample compared to the baseline methods?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "***S1:*** The application of the DDIB framework is an excellent fit for the unpaired nature of the problem. It provides a principled way to bridge the control and perturbed distributions without imposing strong, potentially incorrect, assumptions about cell-to-cell correspondence.\n\n***S2:*** The sparsity masking strategy is a very clever and pragmatic contribution. High-dimensional, sparse data is a major challenge for many generative models, which can easily waste capacity modeling the uninformative zero values. Decoupling the prediction of sparsity from the prediction of expression values is a clean solution that appears to work very well based on the ablation studies.\n\n***S3:*** The work addresses a problem of significant practical importance in drug discovery and functional genomics. Developing more accurate predictive models for perturbation effects has the potential to dramatically accelerate biomedical research. The paper does a good job of motivating the problem and its real-world impact.", "weaknesses": "***W1*** While the DDIB framework is a good fit, the paper does not provide a strong argument for why it is superior to other generative frameworks for unpaired domain translation (e.g., those based on VAEs or GANs, like CycleGAN). A brief discussion contextualizing this choice would strengthen the paper.\n\n***W2*** The model consists of two key parts: the mask model and the diffusion model. The paper evaluates them in ablation studies but does not analyze their interaction. For example, how robust is the diffusion model to potential errors made by the mask model? Does a slightly imperfect mask lead to catastrophic failures or graceful degradation in the generated expression?\n\n***W3*** The model is conditioned on specific perturbation information. While it is tested on unseen perturbations, it's not entirely clear how it would generalize to entirely new classes of perturbations not seen during training. The representation of the perturbation itself seems crucial, and this aspect is not deeply explored.", "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": "HHEmXG4HU7", "reviewer": "Reviewer_DS5U", "summary": "This paper presents Doloris, a generative framework designed to predict single-cell perturbation responses from unpaired data. It uses a dual conditional diffusion implicit bridge (DDIB) to learn separate distributions for control and perturbed cells while connecting them via a shared latent space. To address sparsity, it introduces a separate masking model to predict which genes will be silent, allowing the main diffusion model to focus on modeling active gene signals. The authors demonstrate performance on several public datasets using distributional metrics.", "questions": "See weaknesses.", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "The DDIB-based approach is a reasonable way to model the transition between control and perturbed states without enforcing explicit pairings.", "weaknesses": "- The motivation is unclear, and I don’t think the current motivation has a fair acknowledgement of existing methods. Multiple OT-based perturbation models [1-3], and STATE considers the same problem [4], as well as CellFlow [5]. Variational inference models directly consider sparsity and count distribution [6].\n- I don’t think there are anything related to a negative binomial in your method. The method has nothing to do with ZINB at the moment; therefore, the discussion in Appendix A.6 appears problematic.\n- It is unclear how the results compare to well-established benchmarks in [4, 7]. In particular, linear baselines or simple averaging have shown better performance compared to deep-learning methods in these cases. \n- The paper lacks an ablation study on the value of multi-step inference versus a one-step approach.\n- More comprehensive metrics and evaluations should be employed, e.g., the Cell-eval metrics [4].\n- It is unclear how the ground truth in Fig. 5 is derived, and how the authors distinguish biological and technical zeros.\n\n[1] Bunne, Charlotte, et al. \"Learning single-cell perturbation responses using neural optimal transport.\" Nature methods 20.11 (2023): 1759-1768.\n[2] Klein, Dominik, et al. \"Mapping cells through time and space with moscot.\" Nature 638.8052 (2025): 1065-1075.\n[3] Dong, Mingze, et al. \"Causal identification of single-cell experimental perturbation effects with CINEMA-OT.\" Nature methods 20.11 (2023): 1769-1779.\n[4] Adduri, Abhinav K., et al. \"Predicting cellular responses to perturbation across diverse contexts with State.\" bioRxiv(2025): 2025-06.\n[5] Klein, Dominik, et al. \"CellFlow enables generative single-cell phenotype modeling with flow matching.\" bioRxiv (2025): 2025-04.\n[6] Weinberger, Ethan, Chris Lin, and Su-In Lee. \"Isolating salient variations of interest in single-cell data with contrastiveVI.\" Nature Methods 20.9 (2023): 1336-1345.\n[7] Ahlmann-Eltze, Constantin, Wolfgang Huber, and Simon Anders. \"Deep-learning-based gene perturbation effect prediction does not yet outperform simple linear baselines.\" Nature Methods (2025): 1-5.", "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)