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.

翻译：预训练的扩散模型作为冻结教师，为文本到3D、单步蒸馏和数据归因等下流管道提供支持。这些管道消耗的教师梯度是噪声水平和高斯噪声样本上的蒙特卡洛（Monte Carlo, MC）期望；其估计器方差主导了计算成本，因为每次采样都需要昂贵的上游工作（渲染、模拟、编码）。我们提出CARV，一种计算感知的方差核算框架，该框架激发了分层MC估计器：将昂贵的上游计算摊销到廉价的扩散噪声重采样上，并通过时间步重要性采样和分层逆累积分布函数构造加以锐化。在我们的文本到3D蒸馏和归因实验中，CARV在不改变目标的前提下实现了2-3倍的有效计算乘数（主要来自摊销复用，约25%来自IS+分层）；在单步蒸馏中，相同技术将梯度方差降低了一个数量级，但未改善下游FID，标志着MC方差不再是瓶颈的区间。