Interventional and Counterfactual Inference with Diffusion Models

We consider the problem of answering observational, interventional, and counterfactual queries in a causally sufficient setting where only observational data and the causal graph are available. Utilizing the recent developments in diffusion models, we introduce diffusion-based causal models (DCM) to learn causal mechanisms, that generate unique latent encodings to allow for direct sampling under interventions as well as abduction for counterfactuals. We utilize DCM to model structural equations, seeing that diffusion models serve as a natural candidate here since they encode each node to a latent representation, a proxy for the exogenous noise, and offer flexible and accurate modeling to provide reliable causal statements and estimates. Our empirical evaluations demonstrate significant improvements over existing state-of-the-art methods for answering causal queries. Our theoretical results provide a methodology for analyzing the counterfactual error for general encoder/decoder models which could be of independent interest.