  Inverse design, where we seek to design input variables in order to optimize
an underlying objective function, is an important problem that arises across
fields such as mechanical engineering to aerospace engineering. Inverse design
is typically formulated as an optimization problem, with recent works
leveraging optimization across learned dynamics models. However, as models are
optimized they tend to fall into adversarial modes, preventing effective
sampling. We illustrate that by instead optimizing over the learned energy
function captured by the diffusion model, we can avoid such adversarial
examples and significantly improve design performance. We further illustrate
how such a design system is compositional, enabling us to combine multiple
different diffusion models representing subcomponents of our desired system to
design systems with every specified component. In an N-body interaction task
and a challenging 2D multi-airfoil design task, we demonstrate that by
composing the learned diffusion model at test time, our method allows us to
design initial states and boundary shapes that are more complex than those in
the training data. Our method generalizes to more objects for N-body dataset
and discovers formation flying to minimize drag in the multi-airfoil design
task. Project website and code can be found at
https://github.com/AI4Science-WestlakeU/cindm.
