arXiv:2605.11214cs.LG2026-05

通过自适应调度修正采样时机,提升约束生成质量

Enforcing Constraints in Generative Sampling via Adaptive Correction Scheduling

  • 基于局部几何误差动态分配投影时机,优化约束执行策略
  • 相同修正次数下,准确率提升71.2%,减少75%修正次数
  • 适合需要精确轨迹控制的生成模型设计与部署

生成采样中的硬约束通常通过投影实现,或仅在采样末尾进行,或每步都进行。这种二元方式忽略了根本问题:投影会改变状态分布,进而影响后续更新。因此延迟投影虽能产生可行样本,却可能违背预期采样动态。本文将约束强制视为生成轨迹上的修正调度问题,利用单步约束偏差作为几何不匹配的局部信号,提出自适应修正调度策略——一种依赖状态的动态分配机制,优先在最显著扰动轨迹的步骤上投入修正预算。终端投影与逐步投影均为该方法的极限情形。在受控流形轨迹与学习型投影扩散采样器上验证,自适应调度在相同修正预算下,可恢复71.2%的完整逐步修正收益,同时减少75%的修正次数。结果表明,约束时机是生成采样中的一阶设计变量,仅保证可行性不足以维持预期的约束采样动态。

原文摘要 · Abstract (English)

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.

生成模型约束采样自适应调度

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