Optimal Stochastic Trace Estimation in Generative Modeling

Hutchinson estimators are widely employed in training divergence-based likelihoods for diffusion models to ensure optimal transport (OT) properties. However, this estimator often suffers from high variance and scalability concerns. To address these challenges, we investigate Hutch++, an optimal stochastic trace estimator for generative models, designed to minimize training variance while maintaining transport optimality. Hutch++ is particularly effective for handling ill-conditioned matrices with large condition numbers, which commonly arise when high-dimensional data exhibits a low-dimensional structure. To mitigate the need for frequent and costly QR decompositions, we propose practical schemes that balance frequency and accuracy, backed by theoretical guarantees. Our analysis demonstrates that Hutch++ leads to generations of higher quality. Furthermore, this method exhibits effective variance reduction in various applications, including simulations, conditional time series forecasts, and image generation.

@article{liu2025_2502.18808,
  title={ Optimal Stochastic Trace Estimation in Generative Modeling },
  author={ Xinyang Liu and Hengrong Du and Wei Deng and Ruqi Zhang },
  journal={arXiv preprint arXiv:2502.18808},
  year={ 2025 }
}