Deep generative models reproduce the observational distribution of their training data, inheriting any spurious associations it contains. A common source is an unobserved confounder that shapes both an attribute the user wants to control at sampling time and an attribute expected to vary in response. Existing causal generative approaches resolve the resulting ambiguity by imposing structural assumptions strong enough to single out one interventional distribution; in image domains, such assumptions are rarely warranted, and the data is generally consistent with a set of distinct causal mechanisms -- a feasible region of interventional distributions. We propose CauVaDE (Causal Variational Deep Embedding), built on a canonical augmented SCM in which the unobserved confounder collapses, without loss of generality, into a discrete latent cluster of bounded support while continuous variation is absorbed into independent noises. We prove that this canonical class is dense, in both observational and interventional Wasserstein distance, in the class of augmented SCMs compatible with a given causal diagram, and instantiate it as a mixture variational autoencoder whose cluster variable plays the role of the canonical confounder. An entropy regularizer with weight γ on the cluster posterior then traces a family of candidate causal effects that fit the observational data to comparable likelihood while spanning the feasible region. Experiments on image data benchmarks show that CauVaDE produces diverse interventional samples and improves FID against an unconfounded reference.
Causal generative modeling is essential for developing reliable and transparent AI systems capable of counterfactual reasoning. While existing approaches focus on integrating causal constraints during the training of generative models, they often lack a unified framework to leverage the zero-shot reasoning capabilities of pretrained foundation models. We introduce FM-CGM, a modular framework for end-to-end visual causal reasoning using pretrained foundation models. FM-CGM formalizes the causal pipeline through three core components: a concept extractor, a concept manipulator, and a counterfactual generator. By leveraging a large reasoning model for causal inference and a text-to-image diffusion model for generation, our approach enables zero-shot causal discovery, intervention, and counterfactual generation. We then develop Causal Semantic Guidance (CSG), a cross-attention-based mechanism that ensures semantic interventions propagate to descendant concepts while preserving invariant regions. We empirically show that our approach can identify plausible causal structures and is suitable for faithful counterfactual image generation.
Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.
Generative models for counterfactual outcomes have great potential to support decision-making under complex interventions, but existing approaches are limited by unstable estimation, poor generalization across environments, and bias from nuisance model misspecification. We introduce ADIGen, a framework for automatic, debiased, and invariant counterfactual generation under general interventions, including high-dimensional interventions and outcomes. ADIGen combines Riesz regression to avoid unstable density-ratio estimation, causal invariance to improve generalization under distribution shift, and orthogonal statistical learning to obtain doubly robust guarantees against nuisance model misspecification. We provide excess-risk bounds showing that ADIGen controls counterfactual risk under general interventions, with a product-bias nuisance remainder and an invariant risk bound across environments.