Multi-component 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="AMICI uses multi-headed cross-attention to model how receiver cells integrate information from spatial neighbors by generating query embeddings from learned cell-type-specific parameters that represent receiver identity, while neighboring non-self cells gene expression profiles generate keys and values through neural network embeddings. Attention scores are computed as distance-weighted softmax over query-key products, where each head learns interaction length scales and sender phenotypes, with the model reconstructing masked receiver expression as a residual from cell-type mean using attention-weighted aggregations of neighbor values. Sparsity-inducing penalties on attention weights and value matrices ensure only biologically relevant non-self neighbors contribute.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2025.09.22.677860v1.full.pdf">AMICI</a></td>
           <td>2025</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">Multi-component Disentanglement</span></div></td>

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


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/azizilab/amici" 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 deep generative model that disentangles (multi-omics) single-cell data by separating sources of variation into known and unknown decomposed latent spaces, which are then concatenated for reconstruction. It requires partial supervision through known cell attributes, such as cell type, age, or perturbation, and employs different encoding strategies for categorical and continuous attributes. Biolord maximizes reconstruction accuracy using count likelihoods, along with an additional MSE loss, while minimizing information in the unknown the per-cell embeddings, thus promoting effective disentanglement. To further constrain the unknown latent space, Biolord uses activation penalty (L2) and Gaussian noise.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41587-023-02079-x#Sec6">Biolord</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Unseen Perturbation Prediction</span><span class="badge task-badge">Combinatorial Effect Prediction</span><span class="badge task-badge">Context Transfer</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Probabilistic</span><span class="badge model-badge">ZINB likelihood</span><span class="badge model-badge">Protein-Count (totalVI) Likelihood</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/nitzanlab/biolord" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="CausCell integrates causal representation learning with diffusion-based generative modeling to generate counterfactual single-cell data. It disentangles observed and unobserved concepts using concept-specific adversarial discriminators and links the resulting latent representations through a structural causal model encoded as a directed acyclic graph.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41467-025-62008-1">CausCell</a></td>
           <td>2024</td>

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

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


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/bm2-lab/CausCell" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="CellCap is a deep generative model that extends CPA by incorporating cross-attention mechanisms between cell state and perturbation response (i.e., its basal latent space and the perturbation design matrix). Further, CellCap uses a variational autoencoder (VAE) framework with a linear decoder to identify sparse and interpretable latent factors.">
           <td class="details-control"></td>
           <td><a href="https://www.cell.com/cell-systems/fulltext/S2405-4712(25)00078-X">CellCap</a></td>
           <td>2024</td>

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


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/broadinstitute/CellCap" 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 CPA extension that embeds prior knowlegde about the compound structure of drugs (SMILES representations), allowing it to extend CPA to unseen drug perturbations.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.neurips.cc/paper_files/paper/2022/hash/aa933b5abc1be30baece1d230ec575a7-Abstract-Conference.html">ChemCPA</a></td>
           <td>2022</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Unseen Perturbation Prediction</span><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">Multi-component Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">AE framework inspired by CPA</span><span class="badge model-badge">Chemical representation embeddings</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="github.com/theislab/chemCPA" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Compositional Perturbation Autoencoder (CPA) models single-cell gene expression under perturbations and covariates by decomposing expression into additive latent embeddings: a basal state, perturbation effects, and covariate effects. To ensure that the basal embedding is disentangled, CPA employs an adversarial training approach. Auxiliary classifiers (discriminators) are trained to predict perturbations and covariates from the basal embedding, discouraging the basal representation from encoding such information. To model dose-response effects, CPA uses neural networks to encode continuous covariates and perturbants (e.g., time or dose); whereas combinatorial perturbations are modeled as an additive composition of these embeddings in the latent space.">
           <td class="details-control"></td>
           <td><a href="https://www.embopress.org/doi/full/10.15252/msb.202211517">CPA</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Context Transfer</span><span class="badge task-badge">Combinatorial Effect Prediction</span><span class="badge task-badge">Multi-component Disentanglement</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">DANN-based Adversary that attempts to eliminate treatment effects/ cellular context from latent representation</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/theislab/cpa" 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 disentangles control and pertubed cells into a latent space organized by a causal DAG. The encoder produces a Gaussian latent code z, while an intervention encoder transforms intervention one-hot encodings into two embeddings - a soft assignment vector that targets specific latent dimensions and a scalar capturing the intervention’s magnitude. Multiplying and adding these embeddings to z yields a modified latent vector that simulates a soft intervention, whereas zeroing them recovers the control condition. A causal layer then processes the latent vectors using an upper-triangular matrix G, which enforces an acyclic causal structure and propagates intervention effects among the latent factors. The decoder is applied twice - once to the modified latent code to generate virtual counterfactual outputs that reconstruct interventional outcomes, and once to the unmodified code to recover control samples. This dual decoding forces the model to disentangle intervention-specific effects from the intrinsic data distribution. The training objective combines reconstruction error to reconstruct control samples, a discrepancy loss (e.g., MMD) to align virtual counterfactuals with observed interventional data, KL divergence on the latent space, and an L1 penalty on G to enforce sparsity.">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/forum?id=o16sYKHk3S&noteId=2EQ6cmfPHg">discrepancy-VAE</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Combinatorial Effect Prediction</span><span class="badge task-badge">Causal Structure</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">Disentanglement via Virtual Counterfactuals</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/uhlerlab/discrepancy_vae" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="The Factorized Causal Representation (FCR) framework disentangles cell representations into three latent blocks: z_x, which captures context-specific (covariate) effects and is invariant to treatment; z_t, which encodes direct treatment effects and is invariant to context; and z_{tx}, which represents interactions between treatment and context. It additionally handles interacting covariates by using a variational autoencoder framework augmented with adversarial regularisation. This regularisation enforces the invariance of z_x across treatments and the variability of z_t with respect to covariates. Moreover, the conditional independence of the interaction term z_{tx} from both z_x and z_t, is promoted through permutation-based discriminators.">
           <td class="details-control"></td>
           <td><a href="https://arxiv.org/pdf/2410.22472">FCR</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Seen Perturbation 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">Adversarial</span><span class="badge model-badge">Perturbation-covariate Interactions</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/Genentech/fcr" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="GSFA is a two-layer, guided Factor Analysis model that quantifies the effects of genetic perturbations on latent factors. The model first factorizes the expression matrix Y into a factor matrix Z (normal prior) and gene loadings W (normal-mixture prior). Then, it captures the effect (β) of perturbation on factors using multivariate linear regression. Spike-and-slab prior is used to enforce sparsity on β, which can also analogously be seen as a causal graph. The linearity of GSFA further enables perturbation-associated, differentially-expressed genes to be identified. GSFA uses Gibbs sampling for inference.">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41592-023-02017-4">GSFA</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</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">Factor Analysis</span><span class="badge model-badge">Probabilistic</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/xinhe-lab/GSFA" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="VAE model, which incorporates technical and biological covariates into two sets of latent variables:  - Z_I embeds biologically-relevant variables - Z_B embeds the unwanted variability in the data (i.e. batch effect labels) These are then fed into a shared encoder, along with the count data. The output of this shared encoder is fed to the decoder. Optionally, further disentanglement of the two latent variable sets is achieved by minimizing their total correlation, which is approximated via a minibatch-weighted estimator that quantifies the difference between the joint posterior and the product of individual marginal distributions.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2024.12.06.627196v1.full">inVAE</a></td>
           <td>2024</td>

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


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/theislab/inVAE" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="MultiCPA extends CPA to predict combinatorial perturbation responses from CITE-seq data by integrating gene and protein modalities using either concatenation or a product of experts. It employs totalVI-inspired decoders and likelihoods to model modality-specific outputs.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2022.07.08.499049v1.abstract">MultiCPA</a></td>
           <td>2022</td>

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

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">AE framework inspired by CPA</span><span class="badge model-badge">totalVI likelihood</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/theislab/multicpa" 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 encodes input data into background latent variables and learns sparse, global (salient) embeddings representing the effects of perturbations. These sparse salient embeddings are modeled using a joint relaxed straight-through (Beta-)Bernoulli distribution (mask) and a normally distributed latent space. This method captures perturbation-specific effects as an additive shift to the background representation, analogous to additive shift methods, but it can also be thought as a multi-condition extention to the contrastive framework (limited to two latent variables (case vs. control), to a more general setup capable of learning global embeddings for each perturbation. As in some contrastive methods, for perturbation samples, the perturbation (global) embeddings are added to the background latent variables to reconstruct the data, while for control samples, the perturbation embeddings are effectively set to zero. ">
           <td class="details-control"></td>
           <td><a href="https://proceedings.neurips.cc/paper_files/paper/2023/hash/0001ca33ba34ce0351e4612b744b3936-Abstract-Conference.html">SAMS-VAE</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</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">NB likelihood</span><span class="badge model-badge">Conditional Latent Embeddings</span><span class="badge model-badge">Addative Shift</span><span class="badge model-badge">Sparse Mechanism Shift</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/insitro/sams-vae" 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>
                </a></td>
         </tr>
         <tr data-description="scPRINT is a bidirectional transformer focused for scalable zero-shot inference on new scRNA-seq datasets. It is pre-trained with a composite loss that combines the denoising of downsampled transcripts via a zero-inflated negative-binomial decoder, reconstruction of full expression profiles from bottleneck embeddings, and hierarchical label prediction that disentangles latent factors such as cell type, disease state and sequencing platform. Gene tokens merge a learned protein embedding for the gene ID, an MLP-encoded log-normalised count and a positional encoding of its genomic locus. Pre-training contexts sample 2,200 randomly selected expressed genes per cell (+ padded with unexpressed genes). At inference, cell-specific gene networks are extracted from multi-head attention maps either by averaging all heads or by selecting subsets post hoc based on their correlation with external priors (e.g., PPI databases, ChIP-seq, perturbation-ground-truth networks).">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41467-025-58699-1">scPrint</a></td>
           <td>2025</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">GRN Inference</span><span class="badge task-badge">Multi-component 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">Foundational Gene expression embeddings (from >50M human cells)</span><span class="badge model-badge">BERT-like Bidirectional transformers (with flashattention2)</span><span class="badge model-badge">Self-supervised masked regression</span><span class="badge model-badge">A classifier decoder</span><span class="badge model-badge">ZINB likelihood decoder</span><span class="badge model-badge">PK Representations</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/cantinilab/scPRINT" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="SENA replaces discrepancy‑VAE&#39;s encoder by using a gene-to-pathway mask that applies a soft weighting, via the pathway activity scores α, to the gene expression inputs. In this design, each weight in the encoder is elementwise multiplied by a mask M that assigns full weight to genes known to belong to a pathway and a tunable, lower weight (λ) to genes outside the pathway. This allows the model to primarily capture the signal of annotated genes while still letting unannotated genes contribute, thereby forming interpretable latent factors as linear combinations of pathway activities. ">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/forum?id=NjlafBAahz">SENA</a></td>
           <td>2024</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">Multi-component 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">Discrepancy-VAE architecture</span><span class="badge model-badge">VAE</span><span class="badge model-badge">PK Representations</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/ML4BM-Lab/SENA" 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 Group Factor Analysis for multi-omics data that separates latent variables into guided factors, linked to predefined (observed) variables, and unguided factors. This structure ensures that each observed variable (known biological and technical effects) is captured by a corresponding guided factor, disentangling the observed variables from the residual information, which is in turn captured by the unguided factors. Additionally, SOFA works with both continous and categorical guiding variables and it employs a hierarchical horseshoe prior on loading weights, applying adaptive shrinkage at the view, factor, and feature levels.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2024.10.10.617527v3.full">SOFA</a></td>
           <td>2024</td>

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

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


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/tcapraz/SOFA" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="SpatialDIVA learns distinct latent spaces capturing intrinsic (transcriptomic), morphological (histology), spatial neighborhood, technical (batch), and residual variations. To promote disentanglement, the model employs auxiliary classification heads - using cell type labels to supervise the transcriptomic latent space, pathology annotations to guide the histology latent space, and batch labels to capture technical variation. Additionally, an auxiliary regression head with mean squared error (MSE) loss is trained to ensure that the spatial latent space accurately reconstructs a PCA-based representation derived from concatenated histology and transcriptomic profiles from k-nearest spatial neighbours, thereby capturing both imaging and expression data from adjacent spots.">
           <td class="details-control"></td>
           <td><a href="https://www.biorxiv.org/content/10.1101/2025.02.19.638201v1.full.pdf">SpatialDIVA</a></td>
           <td>2025</td>

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


           <td class="published"><span style="color: #DC143C;">✗</span></td>
            <td><a href="https://github.com/hsmaan/SpatialDIVA" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="Spectra decomposes a gene expression matrix into cell-by-factor and factor-by-gene matrices, while integrating prior knowledge gene sets and cell-type labels. It explicitly models both global and cell-type–specific factors by incorporating cell-type labels, thereby disentagling the typically dominating cell-type variation from shared Gene Programmes. Gene sets are represented as a gene–gene knowledge graph, and a penalty term based on a weighted Bernoulli likelihood, guides the factorisation toward preserving this graph. Yet, it also permits the data-driven discovery of novel programs by &#39;detaching&#39; factors from the prior. Spectra can also include cell-type-specific prior knowledge gene sets (e.g. T cell antigen receptor activation programmes can be limited to T cells)">
           <td class="details-control"></td>
           <td><a href="https://www.nature.com/articles/s41587-023-01940-3">Spectra</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">Multi-component Disentanglement</span></div></td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge model-badge">Poisson Likelihood</span><span class="badge model-badge">Factor Analysis</span><span class="badge model-badge">PK Representations</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/dpeerlab/spectra" 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 combines the sparse mechanism shift from SVAE+ with learning a probabilistic pairing between cells and unobserved auxiliary variables. These auxilary variables correspond to the observed perturbation labels in SVAE+, but here they are learned in a data-driven way (rather than passed as static labels) which in turn enables counterfactual context-transfer scenarios.">
           <td class="details-control"></td>
           <td><a href="https://openreview.net/pdf?id=8hptqO7sfG">svae-ligr</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><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">Causal Structure</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">Sparse Mechanism Shift</span><span class="badge model-badge">Generative/Experience Replay</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/theislab/svaeligr" 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 integrates recent advances in sparse mechanism shift modeling for single-cell data, inferring a causal structure where perturbation labels identify the latent variables affected by each perturbation. The method constructs a graph identifying which latent variables are influenced by specific perturbations, promoting disentaglement and enabling biological interpretability, such as uncovering perturbations affecting shared processes. A key modelling contribution is its probabilistic sparsity approach (relaxed straight-through Beta-Bernoulli) on the global sparse embeddings (graph),  improving upon its predecessor, SVAE. As such, the latent space can be seen as being modelled from a Spike-and-Slab prior.">
           <td class="details-control"></td>
           <td><a href="https://proceedings.mlr.press/v213/lopez23a/lopez23a.pdf">sVAE+</a></td>
           <td>2023</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Seen Perturbation Prediction</span><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Causal Structure</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">Sparse Mechanism Shift</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/Genentech/sVAE" 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 partitions each cell’s latent representation into covariate-specific and covariate-agnostic (invariant) variables. It enforces disentanglement by making the covariate-specific latents more similar for positive pairs of cells (those sharing a covariate) and more dissimilar for negative pairs (those differing in that covariate). Simultaneously, TarDis maximizes or minimizes the distance between these positive/negative pairs and the covariate-agnostic latent space in a way that ensures its independence from the targeted covariates. This is accomplished via multiple distance-based loss terms for each covariate. TarDis supports both categorical and continuous covariates.">
           <td class="details-control"></td>
           <td><a href="https://link.springer.com/chapter/10.1007/978-3-031-90252-9_23">TarDis</a></td>
           <td>2024</td>

           <td><div style="display: flex; flex-wrap: wrap; gap: 0.3em;"><span class="badge task-badge">Multi-component Disentanglement</span><span class="badge task-badge">Context Transfer</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">Multi-modal</span></div></td>


           <td class="published"><span style="color: #2E8B57;">✓</span></td>
            <td><a href="https://github.com/theislab/tardis" class="github-link">
                  <i class="fab fa-github" aria-hidden="true"></i>
                  <span class="sr-only">GitHub</span>
                </a></td>
         </tr>
         <tr data-description="trVAE is a conditional variational autoencoder, which applies Maximum Mean Discrepancy regularization to the first layer of its decoder. This forces the model to learn condition-invariant features, enabling it to transform samples between conditions and predict OOD responses, such as unseen cell-type specific response to seen perturbations. ">
           <td class="details-control"></td>
           <td><a href="https://academic.oup.com/bioinformatics/article/36/Supplement_2/i610/6055927#409207818">trVAE</a></td>
           <td>2020</td>

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

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


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