Abstract: We present a system for generating suggestions from highly-constrained, continuous design spaces. We formulate suggestion as sampling from a probability distribution; constraints are represented as factors that concentrate probability mass around sub-manifolds of the design space. These sampling problems are intractable using typical random walk MCMC techniques, so we adopt Hamiltonian Monte Carlo (HMC), a gradient-based MCMC method. We implement HMC in a high-performance probabilistic programming language, and we evaluate its ability to efficiently generate suggestions for two different, highly-constrained example applications: vector art coloring and designing stable stacking structures.