The Causal Round Trip: Generating Authentic Counterfactuals by Eliminating Information Loss
Rui Wu, Lizheng Wang, Yongjun Li
TL;DR
The paper defines Causal Information Conservation (CIC) as a principle ensuring lossless abduction in structural causal models, identifying Structural Reconstruction Error (SRE) as the key flaw in standard diffusion-based counterfactual generation. It introduces BELM-MDCM, a diffusion framework built around an analytically invertible sampler to achieve zero SRE, and couples it with Targeted Modeling and Hybrid Training to control complexity and inject a causal inductive bias. The work provides formal operator-theoretic foundations, identifiability results, and finite-sample guarantees, and introduces new evaluation metrics (CIC-Score and CMF-Score with CMI-Score and KMD) to assess information conservation and mechanism fidelity. Empirical results on both synthetic and real-data benchmarks show state-of-the-art predictive accuracy, robust counterfactual generation at the individual level, and the ability to perform deeper causal inquiries such as heterogeneity analysis, attribution, and fairness audits. Overall, the paper offers a principled blueprint for reconciling modern diffusion models with classical causal theory, enabling reliable, interpretable, and transportable counterfactual inference.
Abstract
Judea Pearl's vision of Structural Causal Models (SCMs) as engines for counterfactual reasoning hinges on faithful abduction: the precise inference of latent exogenous noise. For decades, operationalizing this step for complex, non-linear mechanisms has remained a significant computational challenge. The advent of diffusion models, powerful universal function approximators, offers a promising solution. However, we argue that their standard design, optimized for perceptual generation over logical inference, introduces a fundamental flaw for this classical problem: an inherent information loss we term the Structural Reconstruction Error (SRE). To address this challenge, we formalize the principle of Causal Information Conservation (CIC) as the necessary condition for faithful abduction. We then introduce BELM-MDCM, the first diffusion-based framework engineered to be causally sound by eliminating SRE by construction through an analytically invertible mechanism. To operationalize this framework, a Targeted Modeling strategy provides structural regularization, while a Hybrid Training Objective instills a strong causal inductive bias. Rigorous experiments demonstrate that our Zero-SRE framework not only achieves state-of-the-art accuracy but, more importantly, enables the high-fidelity, individual-level counterfactuals required for deep causal inquiries. Our work provides a foundational blueprint that reconciles the power of modern generative models with the rigor of classical causal theory, establishing a new and more rigorous standard for this emerging field.