Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling

2026-05-11

AI Summary

This work addresses the challenge in constrained generative sampling where ill-timed constraint enforcement yields samples that satisfy hard constraints yet deviate from desired dynamics. The authors formulate constraint application as a correction scheduling problem along generative trajectories and propose a state-dependent adaptive correction mechanism that dynamically allocates projection resources based on per-step constraint violations and geometric mismatch signals. This approach unifies terminal and stepwise projection strategies and, for the first time, treats the timing of constraint enforcement as a core design variable. Experiments demonstrate that under an identical projection budget, the method achieves 71.2% of the performance gain of full stepwise correction using only 25% of the correction steps, substantially improving the trade-off between computational cost and sampling accuracy.

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.

Problem

• generative sampling
• hard constraints
• projection
• sampling dynamics
• constraint enforcement

Innovation

• adaptive correction scheduling
• constraint enforcement
• generative sampling
• projection budget
• constrained diffusion