Causal Counterfactual Generation

Generative analysis often models multi-domain observations as nonlinear mixtures of domain-invariant content variables and domain-specific style variables. Identifying both factors from unpaired domains enables tasks such as domain transfer and counterfactual data generation. Prior work establishes identifiability under (block-wise) statistical independence between content and style, or via sparse Jacobian assumptions on the nonlinear mixing function, but such conditions can be restrictive in practice. In this work, we introduce content-style differential independence (CSDI), an alternative structural condition requiring that infinitesimal variations in content and style induce orthogonal directions on the data manifold, thereby enabling identifiability even when content and style are dependent and the Jacobian is dense. We operationalize this condition through a blockwise orthogonality constraint on the Jacobian subspaces associated with content and style. To support high-dimensional generative models, we design a stochastic regularizer based on numerical Jacobian approximation, enabling scalable training in settings such as high-resolution image generation. Experiments across multiple datasets corroborate the identifiability analysis and demonstrate practical benefits on counterfactual generation and domain translation.

The geometry of the retinal vessel is a key biomarker of vascular diseases, yet clinical evidence remains primarily observational. Existing generative counterfactuals intervene only at the image-level disease label, failing to isolate explicit anatomical structure. To address this limitation, we propose the Bézier Tree Encoding Counterfactual Framework (BTECF). By abstracting vascular networks into interconnected cubic-Bézier segments, BTECF establishes a disease-agnostic representation in which structural topology is explicitly preserved and atomically perturbable. Coupling this encoding with a diffusion-based generator enables parameter-level do-interventions on explicit geometric axes (e.g., tortuosity, caliber) while preserving background fundus textures. We validate BTECF on diabetic retinopathy, together with independent cohorts for ischemic stroke and Alzheimer's disease. Isolated counterfactual interventions produce dose-responsive shifts in classifier predictions; a matched pixel-drop control attenuates this response by an order of magnitude or more, ruling out out-of-distribution generation artifacts. By enforcing causal isolation between vessel topology and pixel-level confounders, BTECF provides a unified generative paradigm for hypothesis verification across systemic diseases. To support reproducibility, the code will be publicly released upon acceptance.

Distributional causal inference requires estimating not only average treatment effects but also interventional outcome distributions, including quantiles, tail risks, and policy-dependent uncertainty. As a method for distributional causal inference, generative adversarial network (GAN)-based counterfactual methods are flexible tools for this task. However, these methods have several limitations. First, the objectives of certain techniques do not coincide with the statistical risk of the identifiable causal target, and therefore provide limited theoretical guarantees regarding estimable counterfactual distributions or optimality. Second, they tend to rely on unstable density-based methods, such as density ratio estimation. In this paper, we propose GANICE (GAN for Interventional Conditional Estimation) with several advantages: it (i) clarifies the conditional interventional distribution for each treatment--covariate state as the causal estimation target; (ii) estimates the conditional distribution such that its averaged Wasserstein risk is minimized; (iii) establishes minimax optimality. GANICE achieves these advantages through the introduction of the extended Wasserstein distance, the incorporation of a cellwise critic in its dual, and an optimality proof based on Besov space theory. Our experiments demonstrate that GANICE consistently outperforms existing methods.

Estimating counterfactual distributions under interventions is central to treatment risk assessment and counterfactual generation tasks. Existing approaches model the counterfactual distribution as a standalone generative target, without exploiting its relationship to the observational data. In this work, we show that under standard assumptions, observational and counterfactual outcome distributions are tightly linked: they have identical support and tail behavior, remain statistically close under weak confounding, and share any features of high-dimensional outcomes which are invariant to confounders. These properties motivate learning counterfactual distributions not from scratch, but via a deconfounding flow from the observational distribution. We formulate this problem via flow-matching and derive a semiparametrically efficient estimator based on a novel efficient influence function correction. We subsequently extend our estimator to target minimal-energy flows in high-dimensions, which we show can be especially simple targets between observational and counterfactual distributions. In experiments, deconfounding flows outperform existing debiased counterfactual distribution estimators, while also mitigating known failure modes of flow-based methods.

Ascription of an image gives insights into the objects that influence the classification of the whole image or its pixels towards a specific category. These insights help radiologists to visualize deformities in medical imaging. Most of the existing visualization techniques are based on discriminative models and highlight regions of the input image participating in the decision-making of a classifier. However, these approaches do not take all noticeable objects into account as their objective is to classify the input by using a minimal set of discriminative features. To overcome the issue, a counterfactual explanation (CX) based class-oriented feature attribution method is proposed. A counterfactual explanation (CX) explicates a causal reasoning process of the form: "if X had not happened, then Y would not have happened". The method is built on generative adversarial networks (GANs) with a cyclical-consistent loss function. We evaluate our method on three datasets: synthetic, tuberculosis and BraTS. All experiments confirm the efficacy of the proposed method. This study also highlighted the limitations of existing counterfactual explanation techniques in producing plausible counterfactual instances (CIs). Accompanying CXs with believable CIs thus provides self-explanatory analogy-based explanations. To this end, a CI generation method is proposed. Also, a novel technique is used to evaluate the quality of CI. The baseline results are produced on the BraTS dataset.

Structural causal models provide a unified semantics for interventions and counterfactuals, but most identifiability results rely on restrictive assumptions like global monotonicity, which are often violated in embodied interaction, where the same exogenous perturbation can induce opposite responses under different contact contexts. We ask what structure still suffices once global monotonicity is dropped. We introduce non-monotone triangular structural causal models (NM-TM-SCM), which retain triangular recursion but replace global monotonicity with mechanism-wise invertibility and context-independent inverse transport. We prove that these conditions are equivalent to exogenous isomorphism and imply complete counterfactual identifiability, and we give a counterexample showing that local invertibility alone is insufficient. We instantiate the theory in CausalInverter, with triangular invertible layers, orientation gates, and transport-stability regularization. On synthetic non-monotonic mechanisms, the structural bias yields systematic counterfactual gains as non-monotonicity increases. On MuJoCo Door, our model achieves perfect event-level counterfactual recovery, lowers continuous angle error relative to a Transformer baseline, and delivers substantially more stable recovery than Transformer and conditional-flow predictors. On MuJoCo Push, where non-monotonicity is weaker, the same low-data predictors remain competitive or better, consistent with a bias-variance boundary. These results identify a broader identifiable regime between globally monotone triangular models and unconstrained black-box world models.

Most tabular-data generators match marginal statistics yet ignore causal structure, leading downstream models to learn spurious or unfair patterns. We present TabSCM, a mixed-type generator that preserves those causal dependencies. Starting from a Completed Partially Directed Acyclic Graph (CPDAG) found by any causal structure discovery algorithm, TabSCM (i) orients edges to a DAG, (ii) fits root-node marginals with KDE or categorical frequencies, and (iii) learns topologically ordered structural assignments. Such assignments are achieved using conditional diffusion models for continuous variables as child nodes and gradient-boosted trees for categorical ones. Ancestral sampling yields semantically valid records and enables exact counterfactual queries. On seven public datasets, encompassing healthcare, finance, housing, environment, TabSCM matches or surpasses state-of-the-art GAN, diffusion, and LLM baselines in statistical fidelity, downstream utility, and privacy risk, while also cutting rule-violation rates and providing causally meaningful and robust conditional interventions. Because generation is decomposed into explicit equations, it runs up to 583$\times$ faster than diffusion-only models and exposes interpretable knobs for fairness auditing and policy simulation, making TabSCM a practical choice for realism, explainability, and causal soundness.

Verification and validation of cyber-physical systems (CPS) via large-scale simulation often surface failures that are hard to interpret, especially when triggered by interactions between continuous and discrete behaviors at specific events or times. Existing debugging techniques can localize anomalies to specific model components, but they provide little insight into the input-signal values and timing conditions that trigger violations, or the minimal, precisely timed changes that could have prevented the failure. In this article, we introduce DeCaF, a counterfactual-guided explanation and assertion-based characterization framework for CPS debugging. Given a failing test input, DeCaF generates counterfactual changes to the input signals that transform the test from failing to passing. These changes are designed to be minimal, necessary, and sufficient to precisely restore correctness. Then, it infers assertions as logical predicates over inputs that generalize recovery conditions in an interpretable form engineers can reason about, without requiring access to internal model details. Our approach combines three counterfactual generators with two causal models, and infers success assertions. Across three CPS case studies, DeCaF achieves its best success rate with KD-Tree Nearest Neighbors combined with M5 model tree, while Genetic Algorithm combined with Random Forest provides the strongest balance between success and causal precision.

Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial conditions is fundamental to causal inference, domain adaptation, and counterfactual prediction. However, the space of distributions often lacks the vector space structure on which classical methods rely. To address this, we introduce a general notion of parallel dynamics at a distributional level. We base this principle on parallel transport of tangent dynamics along optimal transport geodesics and call it ``Wasserstein Parallel Trends''. By replacing the vector subtraction of classic methods with geodesic parallel transport, we can provide counterfactual comparisons of distributional dynamics in applications such as causal inference, domain adaptation, and batch-effect correction in experimental settings. The main mathematical contribution is a novel notion of fanning scheme on the Wasserstein manifold that allows us to efficiently approximate parallel transport along geodesics while also providing the first theoretical guarantees for parallel transport in the Wasserstein space. We also show that Wasserstein Parallel Trends recovers the classic parallel trends assumption for averages as a special case and derive closed-form parallel transport for Gaussian measures. We deploy the method on synthetic data and two single-cell RNA sequencing datasets to impute gene-expression dynamics across biological systems.

Generating safety-critical driving scenarios requires understanding why dangerous interactions arise, rather than merely forcing collisions. However, existing methods rely on heuristic adversarial agent selection and unstructured perturbations, lacking explicit modeling of interaction dependencies and thus exhibiting a realism--adversarial trade-off. We present CounterScene, a framework that endows closed-loop generative BEV world models with structured counterfactual reasoning for safety-critical scenario generation. Given a safe scene, CounterScene asks: what if the causally critical agent had behaved differently? To answer this, we introduce causal adversarial agent identification to identify the critical agent and classify conflict types, and develop a conflict-aware interactive world model in which a causal interaction graph is used to explicitly model dynamic inter-agent dependencies. Building on this structure, stage-adaptive counterfactual guidance performs minimal interventions on the identified agent, removing its spatial and temporal safety margins while allowing risk to emerge through natural interaction propagation. Extensive experiments on nuScenes demonstrate that CounterScene achieves the strongest adversarial effectiveness while maintaining superior trajectory realism across all horizons, improving long-horizon collision rate from 12.3% to 22.7% over the strongest baseline with better realism (ADE 1.88 vs.2.09). Notably, this advantage further widens over longer rollouts, and CounterScene generalizes zero-shot to nuPlan with state-of-the-art realism.

Judea Pearl's do-calculus provides a foundation for causal inference, but its translation to continuous generative models remains fraught with geometric challenges. We establish the fundamental limits of such interventions. We define the Counterfactual Event Horizon and prove the Manifold Tearing Theorem: deterministic flows inevitably develop finite-time singularities under extreme interventions. We establish the Causal Uncertainty Principle for the trade-off between intervention extremity and identity preservation. Finally, we introduce Geometry-Aware Causal Flow (GACF), a scalable algorithm that utilizes a topological radar to bypass manifold tearing, validated on high-dimensional scRNA-seq data.

Current continuous generative models (e.g., Diffusion Models, Flow Matching) implicitly assume that locally consistent causal mechanisms naturally yield globally coherent counterfactuals. In this paper, we prove that this assumption fails fundamentally when the causal graph exhibits non-trivial homology (e.g., structural conflicts or hidden confounders). We formalize structural causal models as cellular sheaves over Wasserstein spaces, providing a strict algebraic topological definition of cohomological obstructions in measure spaces. To ensure computational tractability and avoid deterministic singularities (which we define as manifold tearing), we introduce entropic regularization and derive the Entropic Wasserstein Causal Sheaf Laplacian, a novel system of coupled non-linear Fokker-Planck equations. Crucially, we prove an entropic pullback lemma for the first variation of pushforward measures. By integrating this with the Implicit Function Theorem (IFT) on Sinkhorn optimality conditions, we establish a direct algorithmic bridge to automatic differentiation (VJP), achieving O(1)-memory reverse-mode gradients strictly independent of the iteration horizon. Empirically, our framework successfully leverages thermodynamic noise to navigate topological barriers ("entropic tunneling") in high-dimensional scRNA-seq counterfactuals. Finally, we invert this theoretical framework to introduce the Topological Causal Score, demonstrating that our Sheaf Laplacian acts as a highly sensitive algebraic detector for topology-aware causal discovery.

Evaluating football player transfers is challenging because player actions depend strongly on tactical systems, teammates, and match context. Despite this complexity, recruitment decisions often rely on static statistics and subjective expert judgment, which do not fully account for these contextual factors. This limitation stems largely from the absence of counterfactual simulation mechanisms capable of predicting outcomes in hypothetical scenarios. To address these challenges, we propose ScoutGPT, a generative model that treats football match events as sequential tokens within a language modeling framework. Utilizing a NanoGPT-based Transformer architecture trained on next-token prediction, ScoutGPT learns the dynamics of match event sequences to simulate event sequences under hypothetical lineups, demonstrating superior predictive performance compared to existing baseline models. Leveraging this capability, the model employs Monte Carlo sampling to enable counterfactual simulation, allowing for the assessment of unobserved scenarios. Experiments on K League data show that simulated player transfers lead to measurable changes in offensive progression and goal probabilities, indicating that ScoutGPT captures player-specific impact beyond traditional static metrics.

We propose sequential transport (ST), a distributional framework for mediation analysis that combines optimal transport (OT) with a mediator directed acyclic graph (DAG). Instead of relying on cross-world counterfactual assumptions, ST constructs unit-level mediator counterfactuals by minimally transporting each mediator, either marginally or conditionally, toward its distribution under an alternative treatment while preserving the causal dependencies encoded by the DAG. For numerical mediators, ST uses monotone (conditional) OT maps based on conditional CDF/quantile estimators; for categorical mediators, it extends naturally via simplex-based transport. We establish consistency of the estimated transport maps and of the induced unit-level decompositions into mutatis mutandis direct and indirect effects under standard regularity and support conditions. When the treatment is randomized or ignorable (possibly conditional on covariates), these decompositions admit a causal interpretation; otherwise, they provide a principled distributional attribution of differences between groups aligned with the mediator structure. Gaussian examples show that ST recovers classical mediation formulas, while additional simulations confirm good performance in nonlinear and mixed-type settings. An application to the COMPAS dataset illustrates how ST yields deterministic, DAG-consistent counterfactual mediators and a fine-grained mediator-level attribution of disparities.

Counterfactual generation for chest X-rays (CXR) aims to simulate plausible pathological changes while preserving patient-specific anatomy. However, diffusion-based editing methods often suffer from structural drift, where stable anatomical semantics propagate globally through attention and distort non-target regions, and unstable pathology expression, since subtle and localized lesions induce weak and noisy conditioning signals. We present an inference-time attention regulation framework for reliable counterfactual CXR synthesis. An anatomy-aware attention regularization module gates self-attention and anatomy-token cross-attention with organ masks, confining structural interactions to anatomical ROIs and reducing unintended distortions. A pathology-guided module enhances pathology-token cross-attention within target lung regions during early denoising and performs lightweight latent corrections driven by an attention-concentration energy, enabling controllable lesion localization and extent. Extensive evaluations on CXR datasets show improved anatomical consistency and more precise, controllable pathological edits compared with standard diffusion editing, supporting localized counterfactual analysis and data augmentation for downstream tasks.

Networks of interdependent industrial assets (clients) are tightly coupled through physical processes and control inputs, raising a key question: how would the output of one client change if another client were operated differently? This is difficult to answer because client-specific data are high-dimensional and private, making centralization of raw data infeasible. Each client also maintains proprietary local models that cannot be modified. We propose a federated framework for causal representation learning in state-space systems that captures interdependencies among clients under these constraints. Each client maps high-dimensional observations into low-dimensional latent states that disentangle intrinsic dynamics from control-driven influences. A central server estimates the global state-transition and control structure. This enables decentralized counterfactual reasoning where clients predict how outputs would change under alternative control inputs at others while only exchanging compact latent states. We prove convergence to a centralized oracle and provide privacy guarantees. Our experiments demonstrate scalability, and accurate cross-client counterfactual inference on synthetic and real-world industrial control system datasets.

The ability to accurately perform counterfactual inference on time series is crucial for decision-making in fields like finance, healthcare, and marketing, as it allows us to understand the impact of events or treatments on outcomes over time. In this paper, we introduce a new counterfactual inference approach tailored to time series data impacted by market events, which is motivated by an industrial application. Utilizing the abduction-action-prediction procedure and the Structural Causal Model framework, we first adapt methods based on variational autoencoders and adversarial autoencoders, both previously used in counterfactual literature although not in time series settings. Then, we present the Conditional Entropy-Penalized Autoencoder (CEPAE), a novel autoencoder-based approach for counterfactual inference, which employs an entropy penalization loss over the latent space to encourage disentangled data representations. We validate our approach both theoretically and experimentally on synthetic, semi-synthetic, and real-world datasets, showing that CEPAE generally outperforms the other approaches in the evaluated metrics.