  We study the relation between supersymmetry and geometric flows driven by the
Bianchi identity for the three-form flux $H$ in heterotic supergravity. We
describe how the flow equations can be derived from a functional that appears
in a rewriting of the bosonic action in terms of squares of supersymmetry
operators. On a complex threefold, the resulting equations match what is known
in the mathematics literature as "anomaly flow". We generalise this to seven-
and eight-manifolds with G$_2$ or Spin(7) structures and discuss examples where
the manifold is a torus fibration over a K3 surface. In the latter cases, the
flow simplifies to a single scalar equation, with the existence of the
supergravity solution implied by the long-time existence and convergence of the
flow. We also comment on the $\alpha'$ expansion and highlight the importance
of using the proper connection in the Bianchi identity to ensure that the
flow's fixed points satisfy the supergravity equations of motion.
