A Causal Bootstrap for Diverse Image Generation under Unobserved Confounding

Deep generative models reproduce the observational distribution underlying the training data, which, in turn, inherit any spurious associations it contains. A common source is an unobserved confounder that simultaneously affects both a treatment attribute the user wants to control/edit (e.g., age, sex) and an observed outcome (e.g., an image) expected to vary in response. Existing causal inference methods resolve the resulting ambiguity by imposing structural assumptions strong enough to single out one interventional distribution. However, in practical domains like image generation, such assumptions are rarely warranted, and the interventional distribution is generally non-identifiable: distinct causal models can agree on the observed data yet imply different causal predictions. This paper proposes CauVaDE (Causal Variational Deep Embedding), a novel family of causal generative models in which the unobserved confounder collapses into a discrete latent cluster with bounded support without loss of generality. We prove that this family can approximate both observational and interventional image distributions with arbitrary accuracy in a canonical latent causal diagram. Building on this model representation, we introduce a novel causal bootstrap that varies the strength of confounder entropy to generate a diverse family of causal explanations, each defining a distinct interventional image distribution. Such a procedure produces distinct interventional images while maintaining a good fit to the observed data.