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arXiv · 2502.18808

Optimal Stochastic Trace Estimation in Generative Modeling

Xinyang Liu·Hengrong Du·Wei Deng·Ruqi Zhang
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Abstract

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.

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Xinyang Liu, Hengrong Du, Wei Deng, Ruqi Zhang. 2025-02-26. Optimal Stochastic Trace Estimation in Generative Modeling. https://arxiv.org/abs/2502.18808

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