Unsupervised Disentanglement
============================


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   <div class="table-container">
     <table id="methods-table" class="display" style="width:100%">
       <thead>
         <tr>
           <th></th><th>Method</th><th>Year</th><th>Task</th>
           <th>Model</th><th>Published</th><th>Code</th>
         </tr>
       </thead>
       <tbody>
         <tr data-description="Celcomen disentangles intra- and inter-cellular gene regulation in spatial transcriptomics data by processing gene expression through two parallel interaction functions. One function uses a single graph convolution layer (1-hop GNN) to learn a gene-gene interaction matrix that captures cross-cell signaling, while the other uses a linear layer to model regulation within individual cells. Training maximises an approximate likelihood that aligns the model-predicted weight matrices to the average gene expression across all cells. Simcomen then leverages these fixed, learned matrices to simulate spatial counterfactuals (e.g., gene knockouts) for in-silico experiments.">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/pdf?id=Tqdsruwyac">Celcomen</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unsupervised Disentanglement</span><span class="badge task-badge">Feature Relationships</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">K-hop Convolution</span><span class="badge model-badge">Spatially-informed</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/Teichlab/celcomen" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="CINEMA-OT disentangles perturbation effects from confounding variation by decomposing the data with independent component analysis (ICA); ICA components correlated with the perturbation labels are identified using Chatterjee’s coefficient and excluded, yielding a background (confounder) latent space that predominantly reflects confounding factors. Optimal transport is then applied to this background space to align perturbed and control cells, thereby generating counterfactual cell pairs, and this OT map is used in downstream analyses. They also propose a reweighting variant (CINEMA-OT-W) to address differential cell type abundance by pre-aligning treated cells with k-nearest neighbor controls and balancing clusters prior to ICA and optimal transport.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41592-023-02040-5#Sec11">CINEMA-OT</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Trace Cell Populations</span><span class="badge task-badge">Perturbation Responsiveness</span><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Unbalanced OT</span><span class="badge model-badge">Entropy-regularized Sinkhorn</span><span class="badge model-badge">ICA</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/vandijklab/CINEMA-OT" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Decipher is a hierarchical deep generative model that integrates and visualises single-cell RNA-seq data from normal and perturbed conditions, identifying shared and disrupted cell-state trajectories. Its architecture includes dual latent spaces: a low-dimensional state for detailed cell-state modeling and a two-dimensional space for visualisation-connected to gene expression through linear or single-layer neural network transformations. The model aligns trajectories by maintaining shared transcriptional programs for common biological processes across conditions.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2023.11.11.566719v2.full">Decipher</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unsupervised Disentanglement</span><span class="badge task-badge">Linear Gene Programmes</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">Linear Decoder</span></div></td>


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/azizilab/decipher" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="A VAE that learns disentangled latent representations in an unsupervised manner by employing additive decoders followed by a nonlinear pooling function (by default, log-sum-exp pooling). The decoder splits the latent vector into K variables, each decoded separately, and then aggregates these outputs. This architecture enforces disentanglement under theoretical assumptions, such as the additivity of independent processes, the existence of process-specific gene markers, and reconstruction quality, ensuring that distinct biological processes map to different latent dimensions. Additionally, DRVI performs batch-correction by optionally incorporating covariate information. Finally, DRVI enables the of ranking latent dimensions based on reconstruction and providing a gene interpretability pipeline via latent variable perturbations.">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/forum?id=8FcsvupyOn">DRVI</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unsupervised Disentanglement</span><span class="badge task-badge">Nonlinear Gene Programmes</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">NB likelihood</span><span class="badge model-badge">Addative Decoders</span><span class="badge model-badge">Multi-modal</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="http://github.com/theislab/drvi" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="MEFISTO extends MOFA+ by incorporating continuous covariates, such as time or spatial coordinates. While MOFA+ assumes that samples are independent and identically distributed, MEFISTO overcomes this limitation by combining the factor analysis framework with Gaussian Processes, which explicitly model the spatio-temporal relationships between samples (cells). MEFISTO can also align samples from different groups (e.g., individuals or species) that have misaligned temporal or spatial profiles.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41592-021-01343-9">MEFISTO</a></td>
           <td>2022</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Linear Gene Programmes</span><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Group Factor Model</span><span class="badge model-badge">Multi-modal</span><span class="badge model-badge">Spatially-informed</span><span class="badge model-badge">Time-resolved</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/bioFAM/MOFA2" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="MichiGAN is a two-step approach that first uses a β-TCVAE - a variant of the variational autoencoder that penalizes total correlation among latent variables to promote disentangled representations. These latent representations (posterior means or samples) are then used to condition a Wasserstein GAN, the generator of which similarly to the VAE reconstructs the data from the latent variables, while attempting to &#39;fool&#39; a discriminator whether the samples were real or generated. Counterfactual predictions are done via latent space arithmetics as in scGEN.">
           <td class="details-control"></td>
           <td><a href="https://link.springer.com/article/10.1186/s13059-021-02373-4">MichiGAN</a></td>
           <td>2021</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unsupervised Disentanglement</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Combinatorial Effect Prediction</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span><span class="badge model-badge">conditioned GAN</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/welch-lab/MichiGAN" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Multi-Omics Factor Analysis v2 (MOFA+) builds builds upon Bayesian Group Factor Analysis, using a matrix factorization approach to infer a low-dimensional representation of typically multi-modal data in the form of latent factors that capture the primary sources of variation across different data types (e.g., RNA expression, DNA methylation) and sample groups. MOFA+ is trained using GPU-accelerated stochastic variational inference which ensures scalability. It also combines Automatic Relevance Determination (ARD) priors, which disentangle variation shared across or unique to specific data modalities and sample groups, with sparsity-inducing spike-and-slab priors on both factors and weights.">
           <td class="details-control"></td>
           <td><a href="https://link.springer.com/article/10.1186/s13059-020-02015-1">MOFA+</a></td>
           <td>2020</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Linear Gene Programmes</span><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Group Factor Model</span><span class="badge model-badge">Multi-modal</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/bioFAM/MOFA2" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="MuVI is a multi-view factor analysis that encodes prior knowledge by imposing structured sparsity on view-specific factor loadings via a weighted, regularized horseshoe prior. Specifically, it uses a weight parameter that controls the variance of each loading; e.g., by default, it is set to 0.99 for genes known to belong to a gene set and 0.01 for genes which do not (are uknown). Using this hieararchical regulairisation strategy, MuVI directly associates latent factors with corresponding gene sets while still allowing for the de novo identification of additional genes relevant to a given factor.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.mlr.press/v206/qoku23a.html">MuVi</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Linear Gene Programmes</span><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Group Factor Model</span><span class="badge model-badge">PK Representations</span><span class="badge model-badge">Multi-modal</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/MLO-lab/MuVI" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="scCausalVI is a causality-aware generative model that disentangles inherent cellular heterogeneity from treatment-induced effects in perturbational single-cell RNA-seq data. It encodes structural causal model (SCM) principles into a deep variational inference framework, learning two distinct but interrelated latent factor sets: background factors capturing intrinsic cellular states and treatment effect factors encoding condition-specific transcriptional changes. A Squeeze-and-Excitation Networks (SENet) attention mechanism adaptively scales treatment effects per cell, enabling cell-state-specific response modeling at single-cell resolution. When batch information is available, scCausalVI simultaneously disentangles batch effects, treatment effects, and baseline cellular states in multi-source data integration. Through cross-condition in silico prediction, scCausalVI predicts gene expression profiles under hypothetical scenarios by intervening on condition assignments within the SCM. This enables identification of treatment-responsive cells via permutation-based significance testing, as well as identification of susceptible versus resistant subpopulations by computationally projecting treated cells back to untreated states. Downstream differential expression and pathway analyses on these virtual cells identified subpopulations reveal molecular signatures and regulatory mechanisms underlying differential cellular responses, facilitating the discovery of therapeutic targets and mechanistic drivers of disease susceptibility. ">
           <td class="details-control"></td>
           <td><a href="https://doi.org/10.1016/j.cels.2025.101443">scCausalVI</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Causal Structure</span><span class="badge task-badge">Unsupervised Disentanglement</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Perturbation Responsiveness</span><span class="badge task-badge">Differential Analysis</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Variational Autoencoder</span><span class="badge model-badge">Structural Causal Model</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/ShaokunAn/scCausalVI" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
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         </tr>
         <tr data-description="SIMVI is a spatially-informed VAE that disentangles gene expression variability into two latent factors: an intrinsic variable z, which captures cell type–specific signals, and a spatial variable s, which quantifies spatial effects. The spatial latent variable s is inferred by aggregating the intrinsic representations of neighboring cells via a Graph Attention Network, thereby incorporating local spatial context. To promote independence between z and s, SIMVI employs an asymmetric regularisation on z using maximum mean discrepancy or, alternatively, a  mutual information estimator, ensuring that z retains minimal non-cell-intrinsic information. Furthermore, leveraging debiased machine learning principles, the model decomposes s using archetypal analysis, and then uses it as the treatment variable and z as confounding covariate, thereby quantifying the specific impact of spatial context on gene expression.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41467-025-58089-7">SIMVI</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Nonlinear Gene Programmes</span><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">ZINB Likelihood</span><span class="badge model-badge">VAE</span><span class="badge model-badge">Spatially-informed</span><span class="badge model-badge">Multi-modal</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/KlugerLab/SIMVI" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Spike and Slab Lasso applied to (non-linear) decoder weights. They show poofs of identifiability when at least 2 &#34;anchor features&#34; are present.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/pdf/2110.10804">sparseVAE</a></td>
           <td>2022</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">VAE</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/gemoran/sparse-vae-code" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="STAMP is an interpretable, spatially-aware dimension reduction method that models the gene expression using Gamma Poisson likelihood, determined by a combination of latent topic proportions (logNormal) ,gene modules, and background residuals. The model employs a structured regularised horseshoe prior on the gene modules to induce sparsity. To incorporate spatial context, STAMP utilises a simplified graph convolutional network as its inference network. STAMP can be extended to handle multi-sample data by adding a batch correction term (via batch-specific loading matrices) and to analyse time-series data by allowing gene modules to vary over time via a Gaussian process prior.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41592-024-02463-8">STAMP</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Linear Gene Programmes</span><span class="badge task-badge">Unsupervised Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Spatially-informed</span><span class="badge model-badge">Time-resolved</span><span class="badge model-badge">Graph encoder</span><span class="badge model-badge">Factor Analysis</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/JinmiaoChenLab/scTM" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
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