Year: 2025
Type: preprint
Abstract: Flow matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets. Independent sampling often yields high-variance estimates, especially when rare but high-impact outcomes dominate the expectation. We propose a non-IID sampling framework that jointly draws multiple samples to cover diverse, salient regions of a flow matching model's generative distribution. To balance diversity and quality, we introduce a score-based regularization for the diversity mechanism (SR), which uses the score function, i.e., the gradient of the log probability, to ensure samples are pushed apart within high-density regions of the data manifold, mitigating off-manifold drift. To enable unbiased estimation when desired, we further develop an approach for importance weighting of non-IID flow samples by learning a residual velocity field that reproduces the marginal distribution of the non-IID samples and by evolving importance weights along trajectories. Empirically, our method produces diverse, high-quality samples and accurate importance-weight estimates and debiased expectation estimates, advancing the reliable characterization of flow matching model outputs.
Source: arXiv (Cornell University)
Authors: Liu, Xinshuang, Li, Runfa Blark, Wei, Shaoxiu, Nguyen, Truong
Institutions: University of San Diego, University of California San Diego
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106657033
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