Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling

TL;DR

This paper introduces adaptive correction scheduling for enforcing constraints in generative sampling, improving feasibility and consistency by dynamically allocating projection steps based on trajectory perturbations.

Contribution

It formalizes constraint enforcement as a correction scheduling problem and proposes an adaptive policy that enhances sampling fidelity with fewer corrections.

Findings

Adaptive scheduling recovers 71.2% of stepwise benefit

Fewer corrections (75% less) achieve similar accuracy

Improves cost-accuracy trade-off in constrained sampling

Abstract

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.