  We develop a novel approach towards causal inference. Rather than structural
equations over a causal graph, we learn stochastic differential equations
(SDEs) whose stationary densities model a system's behavior under
interventions. These stationary diffusion models do not require the formalism
of causal graphs, let alone the common assumption of acyclicity. We show that
in several cases, they generalize to unseen interventions on their variables,
often better than classical approaches. Our inference method is based on a new
theoretical result that expresses a stationarity condition on the diffusion's
generator in a reproducing kernel Hilbert space. The resulting kernel deviation
from stationarity (KDS) is an objective function of independent interest.
