  Accurate estimation of counterfactual outcomes in high-dimensional data is
crucial for decision-making and understanding causal relationships and
intervention outcomes in various domains, including healthcare, economics, and
social sciences. However, existing methods often struggle to generate accurate
and consistent counterfactuals, particularly when the causal relationships are
complex. We propose a novel framework that incorporates causal mechanisms and
diffusion models to generate high-quality counterfactual samples guided by
causal representation. Our approach introduces a novel, theoretically grounded
training and sampling process that enables the model to consistently generate
accurate counterfactual high-dimensional data under multiple intervention
steps. Experimental results on various synthetic and real benchmarks
demonstrate the proposed approach outperforms state-of-the-art methods in
generating accurate and high-quality counterfactuals, using different
evaluation metrics.
