做扩散模型下游应用（如文本到 3D、蒸馏）的团队，如果被梯度方差和计算成本困扰，CARV 的 2-3 倍加速值得直接尝试。
预训练扩散模型常作为冻结教师模型用于下游任务（如文本到 3D、单步蒸馏、数据归因），但这些任务依赖蒙特卡洛期望估计梯度，方差大且计算成本高。本文提出 CARV 框架，通过分层蒙特卡洛估计器，在扩散噪声重采样上摊销昂贵上游计算，结合时间步重要性采样和分层逆 CDF 构造，有效降低方差。在文本到 3D 蒸馏和归因实验中，CARV 实现 2-3 倍有效计算加速，且不改变目标函数；在单步蒸馏中方差降低一个数量级，但下游 FID 无改善，表明此时方差已非瓶颈。该工作为扩散模型下游应用提供了高效方差缩减方案。
Variance Reduction for Expectations with Diffusion Teachers
Pretrained diffusion models serve as frozen teachers feeding downstream pipelines such as text-to-3D, single-step distillation, and data attribution. The teacher gradients these pipelines consume are Monte Carlo (MC) expectations over noise levels and Gaussian noise samples; their estimator variance dominates compute cost because each draw requires expensive upstream work (rendering, simulation, encoding). We introduce CARV, a compute-aware variance-accounting framework that motivates a hierarchical MC estimator: amortize the expensive upstream computation over cheap diffusion-noise resamples, sharpened by timestep importance sampling and a stratified-inverse-CDF construction. In our text-to-3D distillation and attribution experiments, CARV delivers 2-3x effective compute multipliers (most from amortized reuse; ~25% additional from IS+stratification) without changing the objective; in single-step distillation, the same techniques cut gradient variance by an order of magnitude but do not improve downstream FID, marking the regime where MC variance is no longer the bottleneck.