Constrained Generative Modeling

Constrained generative modeling studies how to generate useful samples while respecting requirements such as grammatical rules, molecular validity, physical laws, or safe trajectories. Common approaches include grammar and automaton-based decoding, diffusion and flow-matching methods with projections or primal-dual guidance, and models that build constraints into their representations or training objectives. Applications range from structured text and synthetic data to molecules, motion planning, scientific fields, and engineering design, with evaluation often balancing constraint satisfaction against sample quality, diversity, and computational cost. A central challenge is that enforcing feasibility does not necessarily preserve the model’s intended distribution or uncertainty, so methods must limit bias while remaining efficient and reliable under complex constraints.