1. [Publications](/publications)
2. Variance Reduction for Expectations with Diffusion Teachers

 # Variance Reduction for Expectations with Diffusion Teachers

  ![CARV qualitative trajectory: importance-weighted stratified sampling converges faster than the baseline](/sites/default/files/styles/wide/public/publications/carv_teaser.png?itok=uWJdy5_a)

 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.

 ## Authors

Jesse Bettencourt (NVIDIA)

Xindi Wu (Princeton University and NVIDIA)

Matan Atzmon (NVIDIA)

James Lucas (NVIDIA)

[Jonathan Lorraine](/person/jonathan-lorraine)

 ## Publication Date

Wednesday, May 20, 2026

 ## Published in

[ICML](https://spigmworkshop2026.github.io/)

 ## Research Area

[Artificial Intelligence and Machine Learning ](/research-area/machine-learning-artificial-intelligence)

[Generative AI](/research-area/generative-ai)

 ## External Links

[Paper](https://arxiv.org/abs/2605.21489)

[Project Page](https://research.nvidia.com/labs/sil/projects/CARV/)