Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling
For researchers working on constrained generative sampling, this work shows that constraint timing is a critical design variable, moving beyond the binary choice of terminal vs. stepwise projection.
The paper formalizes constraint enforcement in generative sampling as a correction scheduling problem and introduces adaptive correction scheduling, which allocates projection budget to steps that most perturb the trajectory. Adaptive scheduling recovers 71.2% of full stepwise benefit with 75% fewer corrections, improving the cost-accuracy frontier.
Hard constraints in generative sampling are typically enforced by projection, applied either once at the end of sampling or after every update. This binary framing overlooks a fundamental issue: projection changes the distribution of states which future updates depend on. As a result, delayed projection can produce samples that are feasible but inconsistent with the intended sampling dynamics, even after final projection. We formalize constraint enforcement as a correction scheduling problem over the generative rollout. Using one-step constraint defect as a local signal of geometric mismatch, we introduce adaptive correction scheduling, a state-dependent policy that allocates projection budget to the steps that most strongly perturb the trajectory. Terminal and stepwise projection arise as limiting cases of this family. Across controlled manifold rollouts and a learned projected diffusion sampler, adaptive scheduling improves the cost-accuracy frontier at matched projection budgets, recovering 71.2% of full stepwise benefit with 75% fewer corrections. These results show that constraint timing is a first-class design variable in generative sampling, and that enforcing feasibility alone is insufficient to preserve the intended constrained sampling dynamics.